r 


REESE  LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 

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succession  No.  J  {fO  ^L  &  .   Cla*s  No. 


A 


NEW    ASTRONOMY 


BY 

DAVID    P.    TODD 

M.A.,   PH.D. 

Professor  of  Astronomy  and  Director  of  the  Observatory 
Amherst  College 


*^*«<i&^t4  *<^  /^° ' 

*sw^      I  UNIVERS: 


Copyright,  iSqj.  by  American  Book  Company 


NEW  YORK --CINCINNATI --CHICAGO 

AMERICAN    BOOK    COMPANY 


—  '  Contemplated  as  one  grand  whole,  astronomy  is  the  most 
beautiful  monument  of  the  human  mind,  the  noblest  record  of 
its  intelligence?  —  LA  PLACE 


76-04.6 


3. 


C,  3, 


in  grateful    mrmoru 
of   'Coronet' 


—  l  The  attempt  to  convey  scientific  conceptions,  without  the 
appeal  to  observation,  which  can  alone  give  such  conceptions 
firmness  and  reality,  appears  to  me  to  be  in  direct  antagonism 
to  the  fundamental  principles  of  scientific  education?  — 
HUXLEY 


w.  P.  3 


OF   THK 

UNIVERSITY 


PREFACE 


NEGLECT  hitherto  of  the  availability  of  astronomy  for  a  laboratory 
course  has  mainly  led  to  the  preparation  of  this  New  Astronomy. 
Written  purely  with  a  pedagogic  purpose,  insistence  upon  rightness  of 
principles,  no  matter  how  simple,  has  everywhere  been  preferred  to 
display  of  precision  in  result.  To  instance  a  single  example  :  although 
the  pupil's  equipment  be  but  a  yardstick,  a  pinhole,  and  the  l  rule  of 
three,1  will  he  not  reap  greater  benefit  from  measuring  the  sun  for 
himself  (page  259),  than  from  learning  mere  detail  of  methods  em- 
ployed by  astronomers  in  accurately  measuring  that  luminary  ? 

Astronomy  is  preeminently  a  science  of  observation,  and  there  is  no 
sufficient  reason  why  it  should  not  be  so  studied.  Thereby  will  be 
fostered  a  habit  of  intellectual  alertness  which  lets  nothing  slip.  Six- 
teen years1  experience  in  teaching  the  subject  has  taught  me  many 
lessons  that  I  have  endeavored  to  embody  here.  Earth,  air,  and 
water  (merely  material  things)  are  always  with  us.  We  touch  them, 
handle  them,  ascertain  their  properties,  and  experiment  upon  their 
relations.  Plainly,  in  their  study,  laboratory  courses  are  possible.  So, 
too,  is  a  laboratory  course  in  astronomy,  without  actually  journeying 
to  the  heavenly  bodies ;  for  light  comes  from  them  in  decipherable 
messages,  and  geometric  truth  provides  the  interpretation.  But  the 
student  should  learn  to  connect  fundamental  principles  of  astronomy 
with  tangible  objects  of  the  common  sort,  somewhat  as  in  physics  and 
chemistry ;  and  I  have  aimed  to  indicate  practically  how  teachers  and 
pupils  of  moderate  mechanical  deftness  can  themselves  make  the  appa- 
ratus requisite  for  illustrating  many  of  these  principles.  All  of  it  has 
been  repeatedly  constructed ;  and  its  use  should  pave  the  way  to  better 
equipment  for  more  advanced  study. 

Especial  attention  has  been  accorded  the  recommendations  of  i  The 
Committee  of  Ten1  on  secondary  school  studies  (1892);  the  specifica- 
tions concerning  astronomical  instruction  published  by  the  Board  of 
Regents  of  the  state  of  New  York  (1895);  and  the  Action  of  the 

3 


4  Preface 

Editorial  Board  of  The  Astrophysical  Journal  with  regard  to  Standards 
in  Astrophysics  and  Spectroscopy  (1896). 

In  order  to  secure  the  fullest  educational  value,  I  have  aimed  to 
piesent  astronomy,  not  as  mere  sequence  of  isolated  and  imperfectly 
connected  facts,  but  as  an  inter-related  series  of  philosophic  principles. 
The  geometrical  concept  of  the  celestial  sphere  is  strongly  emphasized ; 
also  its  relation  to  astronomical  instruments.  But  even  more  important 
than  geometry  is  the  philosophical  correlation  of  geometric  systems. 
Ocean  voyages  being  no  longer  uncommon,  1  have  given  rudimental 
principles  of  navigation  in  which  astronomy  is  concerned.  Few  young 
students  may  ever  see  the  inside  of  an  observatory  ;  but  that  is  reason 
for  their  knowing  about  the  instruments  there,  and  prizing  opportuni- 
ties to  visit  such  institutions. 

Everywhere  has  been  kept  in  mind  the  importance  of  the  student's 
thinking  rather  than  memorizing.  Mere  memorizing  should  be  ren- 
dered facile ;  in  treating  of  the  planets,  I  have  therefore  presented  our 
knowledge  of  those  bodies,  not  subdivided  according  to  the  planets 
themselves  as  usually,  but  according  to  especial  elements  and  features. 
The  law  of  universal  gravitation  has  received  fuller  exposition  than 
commonly  in  elementary  books,  its  significance  demanding  this.  Bio- 
graphic notes,  intrusions  in  the  text,  have  been  relegated  to  the  Index. 

In  conclusion,  I  desire  to  thank  Professor  Newcomb  of  Washington, 
Professor  Pickering,  Director  of  Harvard  College  Observatory,  and  my 
colleague.  Professor  Kim  ball,  for  helpful  suggestions  on  the  proof 
sheets.  A  few  illustrations  have  been  reengraved  from  the  Lehrbuch 
der  Kosmischen  Physik  of  Miiller  and  Peters.  For  many  of  the  excel- 
lent photographs,  reader,  publisher,  and  author  are  indebted  to  the 
courtesy  of  astronomers,  in  particular  to  M.  Tisserand,  late  Director 
of  the  Paris  Observatory,  to  the  Astronomer  Royal,  to  Professor  Pick- 
ering, to  Professor  Hale ;  also  to  Dr.  Isaac  Roberts  and  Professor 
Barnard,  both  of  whose  series  of  astronomical  photographs  have  re- 
ceived the  highly  honorable  award  of  the  gold  medal  of  the  Royal 
Astronomical  Society. 

DAVID    P.   TODD. 

AMHERST  COLLEGE  OBSERVATORY. 


CONTENTS 

CHAPTER  PAGE 

I.  INTRODUCTORY        .        .  7 

II.  THE  LANGUAGE  OF  ASTRONOMY 22 

III.  THE  PHILOSOPHY  OF  THE  CELESTIAL  SPHERE       .         .      43 

IV.  THE  STARS  IN  THEIR  COURSES      .  59 
V.  THE  EARTH  AS  A  GLOBE       .                                            .       76 

VI.  THE  EARTH  TURNS  ON  ITS  Axis 97 

VII.  THE  EARTH  REVOLVES  ROUND  THE  SUN        .        .        .131 

VIII.  THE  ASTRONOMY  OF  NAVIGATION 169 

IX.  THE  OBSERVATORY  AND  ITS  INSTRUMENTS     .        .        .     190 

X.  THE  MOON 221 

XL  THE  SUN         ....  ....     255 

XII.  ECLIPSES  OF  SUN  AND  MOON 289 

XIII.  THE  PLANETS 311 

XIV.  THE  ARGUMENT  FOR  UNIVERSAL  GRAVITATION     .        -371 
XV.  COMETS  AND  METEORS  .......     392 

XVI.  THE  STARS  AND  THE  COSMOGONY          .        .  .421 


LIST    OF   COLORED    PLATES 

PLATE  PAGE 

I.     TOTAL  ECLIPSE  OF  THE  SUN.     (From  Himmel  und  Erde, 

edited  by  Dr.  Meyer)       ...        .        .       Frontispiece 

II.  THE   SUN  AS   REVEALED   BY   TELESCOPE    AND   SPECTRO- 

SCOPE.     (From  Annals  of  Harvard  College  Observa- 
tory}           ii 

III.  THE  NORTH  POLAR  HEAVENS 60 

IV.  THE  EQUATORIAL  GIRDLE  OF  THE  STARS         .        .        .      62 

V.     SOLAR  PROMINENCES.     (From  Annals  of  Harvard  College 

Observatory} .         .         .283 

VI.    THREE  VIEWS  OF   MARS,   SHOWING   CHANGING    SEASONS 

OF  HESPERIA.     (Lowell) 360 


ASTRONOMY   FOR   BEGINNERS 


CHAPTER   I 

INTRODUCTORY 


A    STRONOMY  is  the  science  pertaining   to   all   the 

^-^    bodies  of  the  heavens.     Parent  of  the  sciences,  it  is 

the  most  perfect  and  beautiful  of  all.     Sir  William 

Rowan  Hamilton,  the  eminent  mathematician,  has  called  / 

astronomy  man's  golden  chain  between  the  earth  and  the 


The  Yerkes  Observatory,  rrofessor  George  E.  Hale,  Director 

visible  heaven,  by  which  we  '  learn  the  language  and  inter- 
pret the  oracles  of  the  universe.'  This  noble  science  is 
to  man  a  possession  both  old  and  ancestral,  passing  with 
resistless  progress  from  simple  shepherds  of  the  Orient 
watching  their  flocks  by  night,  to  the  rulers  of  ancient 

7 


8  Introductory 

empires  and  the  giants  of  modern  thought;  until  to-day 
the  civilized  world  is  dotted  with  observatories  equipped 
with  a  great  variety  of  instruments  for  weighing  and 
measuring  and  studying  the  celestial  bodies,  each  of  these 
observatories  vying  with  the  other  in  pure  enthusiasm  for 
new  knowledge  of  the  infinite  spaces  around  us. 

Astronomy  a  Useful  Science.  —  Many  devoted  lives  have 
been  grandly  spent  in  pursuit  of  this  branch  of  learning ; 
and  it  would  hardly  be  possible  for  any  one  who  has  given 
even  a  general  glance  at  their  unselfish  history  to  make 
the  vulgar  inquiry,  '  What's  the  use  ? '  Only  a  very  small 
and  unaspiring  mind  ever  asks  this  question  about  any 
science  which  adds  to'the  sum  total  of  our  actual  knowl- 
edge, least  of  all  with  reference  to  this,  —  one  of  the  most 
practical  of  all  sciences.  Astronomy  binds  earth  and 
heaven  in  so  close  a  bond  that  it  even  maps  the  one  by 
means  of  the  other,  and  guides  fleet  and  caravan  over 
wastes  of  sea  and  sand  otherwise  trackless  and  impassa- 
ble. By  faithful  study,  even  for  a  short  time,  it  is  possible 
to  discover  many  of  these  uses.  They  may  not  at  once 
appear  to  put  money  into  men's  pockets  or  clothes  upon 
their  backs ;  but  we  have  passed  the  primitive  stage  of  a 
rudely  toiling  community,  where  material  progress  alone  is 
the  thought  and  aim. 

Especial  Uses.  —  To  specify  in  part  the  relations  in 
which  astronomy  is  useful:  (i)  In  chronology,  —  fixing 
many  disputed  dates  of  ancient  battles,  the  reigns  of  kings, 
and  other  important  historic  events,  and  establishing  the 
exact  length  of  the  units  of  time  requisite  for  the  calendar. 
For  example,  the  surest  basis  of  the  chronology  of  ancient 
Assyria  rests  upon  an  eclipse  of  the  sun  observed  in  Nine- 
veh in  the  middle  of  the  reign  of  Jeroboam  the  Second, 
which  modern  astronomical  calculations  prove  to  have 
taken  place  on  the  i$th  of  June,  B.C.  763.  (2)  In  navi- 


Especial  Uses 


gation,  —  conducting  ships  from  port  to  port,  almost  with- 
out risk,  thereby  saving  human  life  and  lessening  the 
cost  of  many  of  the  necessaries  of  existence.  The  great 
national  observatory  at 
Greenwich  (page  433)  is 
one  of  those  founded  for 
the  especial  and  practical 
purpose  of  improving  the 
astronomical  means  of 
navigation.  (3)  \\\.  geodesy 
and  in  surveying^  —  en- 
abling us  to  ascertain  the 
size  of  the  earth,  make 
accurate  maps  of  its  con- 
tinents and  oceans,  and 
run  boundaries  of  coun- 
tries and  estates.  (4)  In 
determining  exact  time, 

—  a  vast  convenience  in 
all  the  affairs  of  life,  par- 
ticularly in  the  operation 
of    railways.       In    many 
large  cities,  the  dropping 
of  a  ball  on  a  high  tower 
indicates      exact      noon. 

Every  good  watch  has  been  carefully  rated  by  an  accu- 
rate clock  (perhaps  in  some  observatory),  which  again 
has  been  corrected  by  observations  of  the  fixed  stars 

—  a  knowledge  of  the  precise  positions  of  which  depends 
upon  the  faithful  patience  of  a  multitude  of  astronomers 
who   have   given   their   lives   to   this  work   in   the   past. 
Indeed,  it   is   hardly  an    exaggeration    to    say  that  there 
is  no  civilized  person   in  existence  whose   comfort  is  not 
enhanced,    whose   life  is   not   rendered   more   worth   the 


The  Time-ball  at  New  York 


IO 


Introductory 


living,  or  who  is  not  affected,  at  least  indirectly,  by  the 
work  of  astronomers,  and  by  those  who,  though  not 
astronomers,  are  yet  practically  applying  the  principles 
of  this  science  to  the  affairs  of  everyday  life. 

The  Sun  by  Day.  —  Singularly  few  persons  regard  the 
daytime  sky.  Yet  this  beautiful  and  ever-varying  spec- 
tacle may  be  seen 
and  enjoyed  by  all ; 
perhaps  that  is  one 
reason  why  it  is  so 
little  thought  of. 
Even  the  sordid  city 
court,  the  worst 
tenement  district, 
may  have  its  strip 
of  blue  above,  far 
away  from  noise 
and  uncleanliness. 
No  buildings  are 
high  enough  to  shut 
out  this  heavenly 
gift  entirely.  The 
study  of  the  sky  in 
daylight,  especially 
its  clouds,  is  prop- 
erly part  of  a  sepa- 
rate science,  - 
meteorology  as  dis- 
tinguished from  astronomy.  The  marvelous  sun,  too, 
by  which,  as  will  be  seen,  we  live  and  move  and  have 
our  being,  is  held  hardly  less  a  matter  of  course. 
Here  it  is  that  meteorology  joins  on  the  boundary  of  the 
science  we  take  up  to-day ;  for  the  sun  is  one  of  the  chief 
objects  of  study  in  modern  astronomy,  —  its  distance,  its 


Clouds  of  the  Daytime  Sky  (photographed  by  Henry) 


PLATE  II.— THE  SUN  AS  REVEALED  BY  TELESCOPE  AND  SPECTROSCOPE. 

( Trouvelof) 


The  Stars  by  Night 


II 


vast  size,  its  apparent  motion,  the  sources  of  its  intense 
light  and  heat,  its  constantly  changing  spots,  its  constitu- 
tion, the  hydrogen  prom- 
inences, which  seem  to 
spring  from  its  edge  as 
tongue-like   flames,  and 
its    energies,    tirelessly 
radiated  into  space  and 
regnant  in  all  the  forms 
of   life  upon  the  earth, 
no  less  than  in  all  those 
phenomena   of    the    at- 
mosphere which  we  call 
weather.     Many  of  the 
spots    on   the    sun    are 
larger  than   our   globe, 
like   the   one  here    pic- 
tured.    Without  fine  in-  An  Average  Sunspot  (Moreux) 
struments  carefully  adjusted,  the  prominences  cannot  be 
seen  except  during  total  eclipses  of  the  sun: 

The  Stars  by  Night.  --  But  this  sense  of  everyday 
usualness  in  great  part  gives  way,  once  the  sun  has  set, 
and  the  stars  have  come  forth,  as  if  from  their  daytime 
hiding.  Of  course  they  fill  the  sky  just  as  truly  when 
the  world  is  flooded  with  sunlight,  shining  all  in  their 
appointed  places,  where  the  brighter  ones  may  be  seen 
with  the  telescope  during  the  day ;  but  their  feebler  light 
is  conspicuous  only  when  this  greater  brilliance  is  with- 
drawn from  our  horizon,  or  when  the  moon  comes  in 
between  us  and  the  sun,  causing  a  total  eclipse.  Immanuel 
Kant,  a  great  German  philosopher,  has  said  that  two  things 
filled  him  with  ceaseless  awe,  —  the  starry  heavens  above 
and  the  moral  law  within.  Even  the  most  prosaic  cannot 
but  notice  and  revere  the  night-time  sky,  and  few  are  so 


12 


Introductory 


hopelessly  unimaginative  as  not  to  be  impressed  by  the 
dark  blue  dome  spangled  with  its  myriad  stars.  The  posi- 
tions of  the  stars  with  reference  to  one  another  seem  to 
remain  constant,  although  they  are  continually  changing 
their  places  relatively  to  objects  on  the  earth.  Hence  the 
term  fixed  stars.  But  this  is  only  seemingly  the  proper 
expression.  In  reality,  all  are  speeding  through  space  at 


The  Night-time  Sky  in  a  Gre.it  City 

very  high  velocities,  but  so  infinitely  removed  are  the  stars 
from  us  that  they  appear  to  be  at  rest.  Although  quite 
the  reverse,  as  we  now  know,  from  '  fixed,'  the  term  is 
still  used,  because  in  the  astronomically  brief  period  from 
generation  to  generation,  the  changes  are  so  slight  that 
the  naked  eye  is  powerless  to  detect  them. 

Number  of  the  Brighter  Stars.  —  In  ancient  times  the 
brilliant  host  of  the  nightly  sky  was  thought  to  be 
countless  ;  but  surprising  as  it  may  seem,  the  stars  actually 
visible  to  the  unaided  eye  at  a  single  place  in  the  United 
States  do  not  exceed  2000  or  3000,  and  only  upon  ex- 


The  Milky  Way  near  the  Star  15  Monocerotis,  ^R  =  6h.  35  m.,  Decl.  N.  10° 
(photographed  by  Barnard,  1894.    Exposure  3?  hours) 


1 4  Introductory 

ceptionally  favorable  nights  may  so  many  be  counted 
without  a  telescope.  As  an  average,  on  what  may  be 
termed  clear  nights,  the  number  thus  ordinarily  seen  at 
any  given  time  is  rather  less  than  2000 ;  but  this  number 
varies  greatly  with  changing  conditions  of  our  atmos- 
phere. If  one  were  to  keep  count,  through  the  year,  of 
all  the  stars  visible  to  the  naked  eye  in  all  that  part  of 
the  heavens  ever  seen  from  a  single  place  in  the  United 
States,  the  total  number  would  be  about  4000. 

Number  of  the  Telescopic  Stars.  —  By  the  use  of  a  small 
telescope,  or  even  an  opera  glass,  the  number  of  visible 
stars  is  increased  enormously.  Even  in  Galileo's  time,  his 
'  optick  tube '  revealed  an  unsuspected  and  unnumbered 
host,  beyond  the  dreams  of  any  primitive  astronomer. 
With  our  modern  telescopes  (in  which  the  object  glass  of 
almost  every  famous  new  one  has  been  an  advance  in  size 
upon  all  its  predecessors)  the  '  blue  field  of  heaven '  is 
estimated  to  contain  at  least  100,000,000  stars.  Beyond 
what  is  shown  even  by  these  telescopes  are  the  remarkable 
revelations  of  celestial  photography,  which  reproduces 
unerringly  upon  the  sensitive  plate  uncounted  millions  of 
other  stars  too  faint  for  the  eye  to  detect,  even  when  aided 
by  the  most  powerful  optical  means  at  our  command. 
In  a  single  field  embracing  but  a  slight  fraction  of  the 
whole  sky,  recently  charted  with  the  Bruce  telescope  of 
Harvard  Observatory  (the  largest  photographic  instrument 
in  existence),  there  were  counted  no  less  than  400,000  stars. 
And  who  can  say  where  this  stupendous  array  ceases  ? 

The  Constellations.  —  The  names  and  positions  of  the 
brighter  stars  are  very  easy  to  remember.  By  even  a  cas- 
ual glance  at  the  sky  on  any  clear  night,  it  will  be  seen 
that  the  stars  make  all  sorts  of  figures  with  one  another,  — 
squares,  triangles,  half  circles,  —  and  fanciful  combinations 
may  be  traced  in  all  directions.  The  ancients  called  these 


The   Yerkes   Telescope 


The  Yerkes  Telescope  of  the  University  of  Chicago 


This  great  telescope  was  mounted  in  1896-97  at  Williams  Bay,  Wisconsin. 
It  is  the  principal  instrument  of  the  Yerkes  Observatory,  and  cost  about 
$125,000.  The  glasses  for  its  4O-inch  lenses,  the  largest  in  the  world,  were 
made  by  M.  Mantois  of  Paris,  ground  and  figured  by  Alvan  Clark  &  Sons 
of  Cambridgeport ;  and  the  tube  and  all  the  intricate  machinery  for  han- 
dling the  telescope  with  ease  and  precision  were  built  by  Warner  &  Swasey 
of  Cleveland. 


i6 


Introductory 


various  figures  after  their  gods  and  heroes,  dividing  them 
into  48  groups,  largely  named  after  the  characters  asso- 
ciated with  the  voyage 
of  the  fabled  ship  Argo. 
Although  these  constel- 
lations bear  little  real 
resemblance  to  the  men, 
animals,  and  other  ob- 
jects named,  they  too 
are  easily  learned.  Prop- 
erly that  is  not  astron- 
omy, but  merely  geog- 
raphy of  the  heavens ; 
yet  it  is  an  interesting 
and  popular  branch  of 
knowledge,  often  lead- 
ing to  farther  studies 
into  the  most  absorbing 
and  uplifting  of  sciences. 
The  Moon.  —  Of  all 
celestial  bodies,  meteors 
alone  excepted,  the  moon 
is  the  nearest  to  us,  and 
apparently  of  about  the 
same  size  as  the  sun ; 
but  this  is  the  result  of 
a  somewhat  curious  co- 
incidence, by  which  the 
sun,  although  400  times 
larger  than  the  moon,  is 
also  very  nearly  400 

The  Moon  (photographed  by  the  Brothers  Henry*       ^^         f ^^         ^^ 

Even  with  a  small  telescope  we  may  generally  see  the  deep 
craters  and  the  rugged  mountain  peaks  of  the  moon,  partly 


The  Planets  17 

illuminated  by  sunlight,  while  the  rest  of  our  satellite  is 
turned  away  from  the  sun,  lying  in  shadow  and  seen  very 
faintly  by  the  sunlight  falling  upon  it  after  reflection  from 
the  earth.  Our  companion  world  is  dead  and  cold,  its  air 
and  water  almost  certainly  gone,  so  that  no  amount  of 
brightest  sunshine  can  of  itself  bring  back  any  warmth 
of  life.  Earth  and  other  planets  are  dark,  too,  on  the 
surface,  save  for  what  the  sun  bestows  of  brightness  and 
warmth ;  but  our  own  planet  and  some  of  the  others  are 
blessed  with  an  encircling  atmosphere,  best  gift  after 
sunlight  itself,  to  save  and  store  for  our  use  the  sun's  heat 
shed  lavishly  upon  us. 

The  Planets.  —  When  frequent  looking  at  the  nightly 
sky  has  somewhat  familiarized  the  evening  constellations, 
—  different  at  the  same  hour  at  the  various  seasons  of 
the  year,  —  one  may  notice  three  or  four  very  bright 
stars  which  do  not  twinkle.  A  few  evenings'  watching 
will  show  that  they  are  slowly  changing  their  positions 
relatively  to  other  and  fainter  stars  about  them.  These  are 
the  planets  ('wanderers '),  and  will  at  nrst  be  thought  and 
called  stars ;  but  although  speak- 
ing in  the  most  general  terms,  it 
is  proper  to  refer  to  them  as  stars, 
they  are  worlds,  among  which 
the  earth  is  one,  traveling  round 
the  sun  in  nearly  circular  paths. 
Like  our  own  planet,  they  receive 
their  light  from  the  central  orb, 
and  reflect  it  afar.  The  planets 
and  all  their  moons  (called  satel-  jupiter  in  a  small  Telescope 
lites),  as  well  as  our  moon,  give 

light  only  as  reflected  sunshine,  —  second-hand.     Some  of 
the    planets  are  brighter  than    most   stars,  only  because 
they  are  very  much  nearer  to  us  and  to  the  sun. 
TODD'S  ASTRON.  —  2 


i8 


Introductory 


Differences  between  Stars  and  Planets.  —  Besides  the 
noticeable  change  of  position  of  the  planets,  and  their 
shining  by  reflected  light,  another  difference  between 
planets  and  fixed  stars  is  that,  when  seen  through  a  tele- 
scope, planets  appear  larger  in  size  than  with  the  naked 
eye.  This  the  stars  never  do.  Most  planets  have  an 
appreciable  breadth,  called  the  disk;  and  this  seems  to 


The  Planet  Saturn  in  1894  (drawn  by  Barnard  with  the  Lick  Telescope) 

grow  larger  as  the  power  of  telescopes  is  increased.  Stars, 
on  the  contrary,  seem  to  be  mere  points  of  light,  intensely 
luminous,  and  infinitely  far  away.  They  increase  only  in 
brilliancy  with  the  size  of  our  largest  glasses ;  and  even 
the  strongest  lenses  cannot  produce  the  slightest  effect 
upon  the  apparent  size  of  these  stupendously  distant  blaz- 
ing suns.  Also  some  of  the  planets  as  seen  in  the  tele- 
scope show  phases;  in  particular,  Venus,  the  brightest 
planet,  a  familiar  glory  of  the  western  sky,  passing  through 
all  the  changing  phases  of  our  moon,  —  full,  quarter,  and 
crescent.  A  planet  called  Saturn  is  surrounded  by  a 
thin  ring,  as  shown  in  above  engraving.  It  suggested  a 
process  of  evolution  called  the  nebular  hypothesis,  by 
which  stars,  planets,  and  satellites  seem  to  have  devel- 
oped into  present  forms  through  the  operation  of  natural 
laws. 


The  Distances  of  the  Stars  19 

The  Fixed  Stars  are  Suns.  —  All  these  fixed  stars  are 
suns  like  our  own  —  singularly  similar,  the  modern  revela- 
tions of  the  spectroscope  tell  us,  as  to  material  elements 
composing  them.  Probably,  at  their  inconceivable  dis- 
tances from  us,  these  suns  afford  light  and  heat  to 
uncounted  worlds  not  unlike  those  in  the  system  of 
planets  to  which  our  earth  belongs.  But  if  such  planets 
exist,  they  are  too  near  their  own  central  luminaries,  and 
too  faint  for  their  reflected  light  ever  to  reach  our  far-off 
eyes.  One  must  think  of  the  vaster  brilliance  of  the  sun 
as  due  almost  wholly  to  our  relative  .  nearness  to  him. 
Were  the  earth  to  be  removed  as  far  from  the  sun  as 
it  is  distant  from  the  stars,  our  lord  of  day  would  shrink 
to  the  feeble  insignificance  of  an  average  star. 

The  Distances  of  the  Stars.  —  The  nearest  star  is  so  far 
from  us  that  its  distance  in  figures,  however  expressed, 
remains  unapprehended  by  the  human  mind.  Who  can 
conceive  of  25  millions  of  millions  of  miles?  Yet  so  re- 
mote is  our  closest  stellar  neighbor.  As  the  stars  vary 
enormously  in  their  distances  from  us,  so  they  are  equally 
diverse  in  their  relations  to  each  other.  We  see  them  all 
by  the  light  they  emit  —  light  which  does  not  come  to  us  in- 
stantaneously, yet  with  speed  almost  inconceivably  great. 
While  one  is  taking  two  ordinary  steps,  at  an  average 
walking  pace,  light  will  travel  a  distance  equal  to  eight 
times  round  the  world  (nearly  200,000  miles).  Now,  to 
realize  in  some  sense  the  enormous  distance  of  the  nearest 
fixed  star  from  our  earth,  open  a  Webster's  International 
Dictionary,  which  contains  over  2000  pages  of  three  col- 
umns each,  or  the  equivalent.  Begin  to  read  as  rapidly  as 
you  can,  and  imagine  a  ray  of  light  to  have  just  left  the 
nearest  fixed  star  at  the  instant  you  began.  By  the  time 
you  have  finished  a  single  page,  the  star's  light  will  have 
sped  onward  toward  the  earth  no  less  than  100,000,000  miles. 


OF 

TTT'JTVP.'RGT'TV 


20 


Introductory 


Imagine  that  you  could  keep  right  on  reading,  tirelessly 
and  without  ceasing,  day  and  night,  just  as  light  itself 
travels  —  how  many  pages  would  you  have  read  when  the 
ray  of  light  from  Alpha  Centauri,  the  nearest  fixed  star, 
had  reached  the  earth  ?  You  would  have  read  it  com- 
pletely through,  —  not  once,  or  twice,  but  nearly  a  hundred 
times.  So  enormously  distant  is  this  nearest  of  the  stars 
that,  if  it  were  blotted  out  of  existence  this  present  mo- 
ment, it  would  continue  to  shine  in  its  accustomed  place 
for  more  than  three  years  to  come.  And  other  stars  whose 
distances  have  been  measured  are  a  hundredfold  more 
remote. 

The  Shooting  Stars  and  Comets.  —  Very  frequent  celes- 
tial sights,  especially  in  April,  August,  and  November,  are 

the  swarms  of  swiftly-falling 
meteors.  They  flash  across 
the  sky  and  seem  to  vanish 
into  the  blackness  whence 
they  came,  burning  sparks  in 
the  starry  firmament.  On 
rare  occasions  a  fragment  of 
a  meteor  falls  down  upon  the 
surface  of  the  earth,  and  many 
thousands  of  such  specimens 
are  preserved  as  collections 
of  meteorites  in  various  scien- 
tific centers,  —  Vienna,  Lon- 
don, Paris,  and  Washington. 
Sometimes  they  are  of  iron, 
and  sometimes  of  stone. 
Much  less  common  than  the 
spectacle  of  shooting  stars 

is  that  of  a  majestic  comet,  whose  long  and  graceful  tail 
sweeps  many  degrees  along  the  sky,  sometimes  for  weeks 


The  Great  Comet  of  1858 


Gravitation  2 1 

or  even  months  together.  All  these  wandering  visitors, 
too,  must  be  studied  in  their  place. 

General  Outline.  —  We  know  that  the  stars  are  suns ; 
that  our  sun  is  one  of  them,  seemingly  larger  only  because 
very  much  nearer;  that  he  conducts  with  him  through 
space  our  earth  and  her  companion  planets  with  their 
moons,  or  satellites ;  that  the  stars  are  all  moving  through 
the  celestial  spaces  with  great  velocity,  though  at  such 
enormous  distances  from  us  that  they  appear  to  be  almost 
at  rest ;  that  meteors  and  comets  flash  into  our  firmament, 
the  former  to  perish  after  one  bright,  sparkling  clash  with 
our  atmosphere,  while  the  latter  have  their  known  and 
regular  orbits,  or  paths,  some  of  them  coming  back  within 
our  sight  at  predicted  intervals. 

Gravitation. — The  mighty  power  called  gravitation  holds 
all  these  whirling,  flying,  incandescent  or  white-hot,  or 
cold  and  dead  bodies  from  swerving  outside  their  paths 
in  space ;  and,  little  by  little,  the  patience  and  ingenuity 
and  genius  of  man  have  interpreted  many  of  the  laws 
governing  them,  and  have  brought  to  our  knowledge 
manifold  facts  about  them,  —  their  weights  and  distances, 
sizes  and  motions,  and  even  the  elemental  substances  of 
which  they  are  composed.  Their  physical  appearances, 
as  revealed  by  telescope  and  camera,  will  be  abundantly 
emphasized.  But  perhaps  the  most  striking  fact  in  all 
astronomy  is  that  unerring  precision  with  which  the 
heavenly  bodies  move  through  the  celestial  spaces  in  ac- 
cordance with  this  great  law  of  gravitation,  whose  action 
enables  us  to  foretell  with  great  accuracy,  hundreds  of 
years  in  advance,  the  places  of  planets  in  the  starry 
heavens,  and  the  exact  hour,  minute,  and  second,  when 
eclipses  will  happen.  And  progress  through  the  chapters 
of  this  book  will  unfold  in  part  the  knowledge  gained  by 
astronomers  through  centuries  of  careful  investigation. 


CHAPTER  II 

THE  LANGUAGE  OF  ASTRONOMY 

NO  one  can  understand  even  the   simplest  truths  of 
astronomy  without  first  learning  the  language  of  pre- 
cision which  astronomers  use.     Only  a  few  terms  in 
this  language  will  be  necessary  at  the  outset,  and  they  will 
be  illustrated  and  ideas  of  them  conveyed  by  means  of  corn- 


How  to  find  True  North  (Approximately) 

mon  objects  and  simple  processes.  First,  the  four  cardinal 
points,  east,  north,  west,  and  south,  —  terms  in  constant 
use  from  the  remotest  antiquity. 

22 


Plumb-line,  Zenith,  and  Nadir 


How  to  find  the  Cardinal  Points.  —  Any  sharply-pointed  object, 
firmly  set,  may  be  used  as  a  gnomon  for  finding  the  cardinal  points. 
But  the  following  method  has  greater  advantages.  Place  a  carefully 
leveled  board  or  table  so  that  the  sun  may  fall  freely  upon  it,  from 
about  nine  o'clock  in  the  morning  until  three  in  the  afternoon.  Fasten 
securely.  Near  the  sunward  end  of  the  table,  and  about  eight  inches 
above  it,  fix  firmly  a  card  with  a  smooth  pin  hole  through  it.  This  will 
give  a  small,  oval  image  of  the  sun  on  the  table,  and  its  position  must 
be  marked  at  nine  o'clock,  at  a  quarter  past,  and  at  half  after  nine ; 
again  at  half  after  two  in  the  afternoon,  a  quarter  to  three,  and  three 
o'clock.  The  principle  involved  is  that  of  the  gnomon  of  Anaximander 
in  very  compact  form.  Take  especial  care  that  the  marked  surface, 
whether  board  or  paper,  shall  not  have  moved  meanwhile.  Draw  three 
straight  lines  joining  the  sun  marks,  as  indicated  in  the  picture  oppo- 
site ;  connect  the  nine  o'clock  mark  with  the  three  o'clock  one;  draw 
a  second  line  connecting  the  9:15  mark  with  that  made  at  2  : 45  ;  and 
a  third,  joining  the  9  :  30  and  2  : 30  marks.  These  three  lines  will  be 
nearly  parallel,  and  they  mark  the  direction  east  and  west  approxi- 
mately, the  east  end  being  indicated  by  the  three  afternoon  marks. 
Three  pairs  of  points  are  better  than  one,  because  clouds  may  interfere 
with  the  afternoon  observations ;  also,  we  can  take  the  average  direc- 
tion of  three  lines,  which  will  give  true  east  and 
west  more  accurately  than  a  single  line.  By  the 
simple  construction  in  geometry  indicated  in  the 
illustration,  draw  a  perpendicular  to  this  average 
line ;  this  perpendicular,  then,  will  lie  in  the  direc- 
tion north  and  south,  north  lying  on  the  right 
hand  as  one  faces  west.  Extend  these  two  straight 
lines  indefinitely,  and  they  will  mark  the  four  car- 
dinal points  called  east,  north,  west,  and  south. 

Plumb-line,  Zenith,  and  Nadir.  —  Suspend  any 
heavy  object  by  a  delicate  cord  attached  to  a  firm 
support,  and  allow  it  to  come  to  rest.     Draw  it  to 
one  side  or  the  other  from  its  support,  and  let  it 
swing  freely.    Such  an  object  capable  of  swinging  is 
called  a  pendulum.    The  force  causing  it  to  swing 
back  and  forth  is  called  the  attraction  of  gravity. 
We   shall   see   subsequently  that  this  is  the  same 
force  that  makes  all  bodies  fall  to  the  earth ;  also 
that  it  holds  the  moon,  our  satellite,  in  its  monthly 
path,  or  orbit,  about  us.     After  swinging  back  and  forth  many  times, 
the  pendulum  will  come  to  rest ;  and  it  will  do  so  more  quickly  if  the 
weight  or  bob  of  the  pendulum  is  freely  suspended  in  a  basin  of  water. 
A    pendulum    that    has    stopped    swinging    becomes    a    plumb-line. 


A  Plumb-line 


24  The  Language  of  Astroncmy 

Imagine  the  cord  of  the  plumb-line  extended  both  upward  to  the  sky 
and  downward  through  the  earth  indefinitely.  The  point  overhead 
where  the  plumb-line  intersects  the  sky  is  called  the  zenith ;  the  oppo- 
site point  is  called  the  nadir. 

The  Apparent  or  Visible  Horizon.  —  Looking  up  to  the 
sky,  it  seems  to  be  arched  over  us  like  the  inside  of  a  great 
hollow  sphere.  The  dome  of  the  sky  is  nearly  hemispher- 
ical, and  seems  to  most  eyes  less  distant  overhead.  In 
ordinary  inland  regions  the  sky  seems  to  meet  the  earth 
in  an  irregular  and  broken  line.  This  is  called  the  appa- 


Plane  of  the  Sensible  Horizon  cuts  through  the  Mountains 

rent  or  visible  horizon ;  and  nearly  every  point  of  it,  even 
in  locations  not  especially  mountainous,  will  usually  be 
considerably  above  the  level  of  the  eye.  In  cities  the 
surrounding  buildings,  the  trees  in  the  park,  and  the  spires 
of  churches  will  lift  themselves  into  our  vision,  too  near  by 
to  allow  any  observation  of  the  sky  at  the  exact  level  of 
the  eye.  In  the  country,  in  Massachusetts,  for  example, 
it  is  not  always  easy,  without  ascending  some  great 
height,  to  reduce  the  obstacles  forming  the  apparent  hori- 
zon to  a  minimum ;  and  usually  the  sensible  horizon  lies 
far  below  them  all.  Objects  relatively  near,  then,  whether 


The  Sensible  Horizon  25 

houses,  grain  elevators,  churches,  forests,  or  mountains, 
make  irregular  curves  and  broken  lines  which  limit  the 
outward  view  in  every  direction.  Their  outline  marks  the 
observer's  apparent,  or  local,  or  visible  horizon. 

The  Sensible  Horizon.  —  From  the  surface  of  the  ocean,  or  from  a 
widely  extended  plain  or  prairie,  the  dome  of  the  sky  appears  to  join 
the  earth  in  a  nearly  perfect  circle  about  25  miles  in  diameter.  In  Bos- 
ton, for  instance,  we  may  take  the  steamer  for  Nahant,  and  for  a  portion 
of  even  that  short  trip  our  perfect  ocean  horizon  on  one  side  will  hardly 


The  Visible  Horizon  on  the  Ocean 

be  interfered  with.  In  New  York  a  boat  trip  to  Far  Rockaway  or  Long 
Branch  will  give  us  a  similar  opportunity.  In  Chicago  we  have  a  choice 
of  ways  to  get  a  complete  view  of  the  sensible  horizon.  A  car  ride 
in  almost  any  direction  —  to  Evanston,  perhaps  — will  show  widely 
extended  prairies,  seeming  to  stretch  to  the  sky  on  all  sides ;  far  out 
upon  Lake  Michigan,  the  effect  upon  the  observer  is  like  that  of  the 
ocean ;  or  perchance  the  Auditorium  tower  may  be  ascended,  and  if  the 
distant  view  is  clear,  a  far-away  horizon  of  the  sensible  order  is  within 
sight.  Practically  in  this  circle,  the  four  cardinal  points  are  located. 
Imagine  a  plane  passed  through  these  four  points.  It  will  pass  through 
the  eye  of  the  observer,  and  will  essentially  be  the  plane  of  his  sensible 
horizon,  neglecting  only  a  small  angle  called  the  dip  of  the  horizon,  a 


26  The  Language  of  Astronomy 

term  used  in  navigation,  and  explained  in  a  later  chapter.  On  a  small 
piece  of  cardboard  draw  two  lines  at  right  angles,  one  of  them  being 
near  the  middle  of  the  card.  Pierce  the  card  at  each  end  of  this  line, 
and  draw  a  piece  of  twine  through  the  holes.  Fasten  one  end  of  the 
twine  to  some  firm  object,  and  suspend  a  weight  of  a  few  pounds  by  the 
other  end.  When  the  pendulum  has  come  to  rest,  fasten  the  bottom 
of  the  plumb-line  carefully  in  that  position,  and  stretch  it  taut.  Then 
twirl  the  card  round,  and  the  second  line  on  it  will  point  everywhere 
in  the  direction  of  the  sensible  horizon. 


The  sensible  horizon,  then,  is  a  plane  passing  through 
the  point  of  observation  and  perpendicular  to  the  plumb- 
line.  When  the  term  horizon  alone  is  used,  the  sensible 
horizon  is  meant.  It  is  a  fundamental  plane  of  reference 
in  astronomical  measurement. 

The  Terrestrial  Sphere.  —  A  sphere  is  a  solid  figure  all 
points  on  whose  surface  are  at  the  same  distance  from  a 

point  within  called  the 
center.  The  general 
figure  of  the  earth 
being  spherical,  it 
will  be  seen  that  the 
directions  indicated 
by  the  terms  north, 
south,  east,  and  west, 
if  extended  in  straight 
lines  into  space,  are 
true  only  for  a  given 
locality,  or  position  of 
the  observer.  This  is 
because  he  is  situated 
upon  the  surface  of 
a  globe  or  sphere, 
and  the  moment  he 

changes  his  position  upon  it,  his  zenith  and  horizon  and 
system  of  cardinal  points  all  change  with   him.      Down 


Properties  of  the  Celestial  Sphere  27 

always  means  toward  the  center  of  this  globe ;  so  that 
if  a  plumb-line  were  imagined  as  extended  downward 
through  the  earth,  at  the  antipodes  it  would  coincide  with 
the  direction  ///.  If  we  go  to  the  opposite  side  of  the 
globe,  changing  our  longitude  by  180°,  evidently  the  direc- 
tions called  east  by  us  in  these  two  remote  localities  will 
be  exactly  opposite  to  each  other  in  space.  So  that  a  con- 
tinuous line,  in  order  to  represent  a  constant  direction, 
must  have  a  constant  curvature,  corresponding  to  that  of 
the  surface  of  the  earth.  The  plane  passing  through  the 
earth's  center  parallel  to  the  sensible  horizon  is  called  the 
rational  horizon. 

The  Celestial  Sphere.  —  We  have  spoken  about  the  hemi- 
sphere or  dome  of  the  sky.  It  is  obvious  from  geometry 
that  the  hemisphere  above  the  sensible  horizon  must  be 
matched  by  an  equal  hemisphere  inverted,  and  lying  below 
it.  This  complete  and  regular  form,  made  by  the  two 
hemispheres  joined,  is  called  the  celestial  sphere.  Sun, 
moon,  and  all  the  stars  of  the  firmament  are  scattered 
apparently  at  random  upon  its  inner  surface.  We  need 
not  now  concern  ourselves  about  the  remoteness  of  the 
bodies  in  the  sky.  All  appear  to  be  at  the  same  distance 
from  us  ;  and  the  eye  unaided  is  powerless  to  find  out  what 
that  distance  is.  But  evidently  there  may  be  a  very  great 
range  in  their  distances,  just  as  there  is  in  the  lights  of 
different  sizes  on  ships  in  a  harbor,  or  in  the  night  signals 
along  a  straight  stretch  of  railway  in  or  near  a  great  city. 
In  either  case,  on  a  dark  night,  an  inexperienced  person 
has  little  to  guide  him  safely  in  judging  what  the  distances 
and  relative  location  of  the  lights  may  be. 

Properties  of  the  Celestial  Sphere.  —  The  celestial  sphere, 
notwithstanding  its  inconceivable  magnitude,  possesses  all 
the  properties  of  a  geometric  sphere :  not  only  is  every 
point  of  its  surface  equally  distant  from  a  point  within 


28  The  Language  of  Astronomy 

called  its  center  (the  point  where  the  observer  is),  but  all 
planes  cutting  the  sphere  through  its  center  trace  out  cir- 
cles of  equal  magnitude  upon  its  surface.  These  are  called 
great  circles.  All  planes  cutting  the  sphere  otherwise 
than  through  its  center  trace  out  small  circles  upon  its 
surface.  Evidently  it  is  possible  to  imagine  upon  any 
sphere  as  many  great  circles  and  as  many  small  circles  as 
may  be  desired.  Three  systems  of  circles  of  the  celestial 
sphere,  with  their  related  points,  lines,  and  arcs,  are  in 
common  use.  They  are  : 

(A)  the  Horizon  System, 

(B)  the  Equator  System, 

(C)  the  Ecliptic  System. 

(A)  The  Horizon  System. — The  great  circle  that  passes 
through  the  four  cardinal  points  is  called,  as  we  have 
seen,  the  horizon.  Upon  it  is  based  a  system  of  circles 
of  the  celestial  sphere  much  used  in  astronomical  de- 
scriptions and  measurements.  Any  great  circle  traced  on 
the  celestial  sphere  by  a  vertical  plane  passing  through 
the  point  of  observation  is  called  a  vertical  circle.  Clearly 
an  indefinitely  great  number  of  vertical  circles  may  be  imag- 
ined as  drawn.  The  planes  of  all  vertical  circles  intersect 
each  other  in  a  vertical  line  —  the  plumb-line  extended,— 
joining  zenith  and  nadir.  Two  vertical  circles  are  very 
frequently  used,  and  have  especial  names  :  first,  the  vertical 
circle  passing  through  the  north  and  south  points  of  the 
horizon  is  the  meridian;  second,  the  vertical  circle  at 
right  angles  to  the  plane  of  the  meridian,  and  passing 
through  the  east  and  west  points  of  the  horizon/ is  called 
the  prime  vertical.  Any  small  circle  of  the  celestial  sphere 
cutting  it  parallel  to  the  horizon  is  called  an  almucantar. 
Evidently  there  is  no  limit  to  the  number  of  almucantars ; 
one  may  be  imagined  as  drawn  through  every  star  in  the 


Change  of  Horizon  System 


29 


sky.  The  nearer  a  star  is  to  the  zenith,  the  smaller 
its  almucantar,  just  as  parallels  of  geographic  latitude 
upon  the  earth  be- 
come smaller  and 
smaller  as  the  poles 
are  approached. 
Three  hoops  of  a  bar- 
rel tied  or  tacked  to- 
gether, with  all  the 
angles  right  angles, 
as  in  the  illustration, 
form  an  excellent  rep- 
resentation of  horizon, 
meridian,  and  prime 
vertical;  a  much 
smaller  hoop  (near 
the  top)  may  illustrate 
an  almucantar.  Such 
a  concrete  model  is  a 

necessary  aid  to  many  minds  in  attaining  an  adequate  con- 
ception of  the  abstract  circles  of  the  celestial  sphere. 
Essentially  they  are  a  pattern  of  the  armillary  sphere  of 
the  ancient  astronomy. 

Change  of  Horizon  System  with  Change  of  Place.  —  The 
terms  horizon,  meridian,  prime  vertical,  and  almu- 
cantar are  generally  applied  to  the  circles  upon  the 
celestial  sphere  traced  by  their  planes.  The  terms  are, 
however,  often,  and  properly,  employed  to  designate 
the  planes  themselves.  It  will  be  understood  that  these 
four  terms  apply  to  an  observer  wherever  he  may  be 
located  upon  the  surface  of  the  earth.  If  he  remains  in 
a  single  position,  or  has  an  observatory  with  a  single 
instrument,  his  horizon  plane,  meridian,  and  other  circles, 
planes,  and  points  connected  with  it,  have  always  a  con- 


Chief  Circles  of  Horizon.  System  (A), 


30  The  Language  of  Astronomy 

stant  and  definite  position,  relative  to  the  observer  him- 
self. They  are  imaginary  planes  and  circles  which  the 
observer  carries  about  with  him  wherever  he  goes.  The 
moment  he  changes  his  locality,  by  so  much  even  as  a 
few  feet,  he  has  thereby  changed  the  position  of  all  this 
network,  or  system  of  celestial  circles,  by  an  amount 
small,  to  be  sure,  but  readily  measurable  by  the  instru- 
ments and  methods  of  the  modern  astronomer. 

Diurnal  Motion  and  the  Diurnal  Arc.  —  The  sun,  moon, 
and  stars,  in  their  everyday  motion,  appear  to  cross  these 


«SS£ 

The  Midsummei  cun  is  Highest  and  its  Diurnal  Arc  is  Longest 

circles  in  various  directions,  and  at  various  angles,  and 
with  various  velocities.  A  few  evenings'  observation  will 
show  this.  These  movements  are  known  as  the  phe- 
nomena of  the  diurnal  motion.  Observe  the  points  where 
the  sun  rises  and  sets ;  if  in  the  latter  half  of  September 
or  March,  these  will  be  found  to  be  almost  due  east  and 


Diurnal  Motion  of  a  Star  Overhead         31 

west.  As  noon  approaches,  near  which  time  the  sun 
will  cross  the  meridian,  his  course,  in  the  latitude  of  the 
United  States,  will  be  found  to  have  been,  not  upward 
along  the  prime  vertical,  but  obliquely  toward  the  south, 
as  illustrated :  his  paths  at  various  seasons  are  all  in 
parallel  planes.  He  will  reach  the  highest  point  when 
crossing  the  meridian,  and  is  then  said  to  culminate. 
Onward  to  sunset  he  describes  an  arc  almost  precisely 
symmetrical  with  the  forenoon  path.  This  apparent  track 
of  the  sun  through  the  daytime  sky,  from  sunrise  to  sun- 
set, is  called  the  diurnal  arc ;  and  either  half  of  it,  between 
meridian  and  horizon,  is  called  the  semidiurnal  arc.  Simi- 
larly observe  the  moon. 

Perhaps  it  will  rise  considerably  north  of  east.  Watch  it  as  it 
mounts  to  the  meridian.  It  will  cross  this  plane  only  a  few  degrees 
south  of  the  zenith,  and  descend  the  western  half  of  its  diurnal  arc, 
setting  about  as  far  north  of  true  west  as  it  rose  north  of  true  east. 
Select  very  bright  stars  in  other  parts  of  the  sky  both  north  and  south 
of  sun  and  moon,  and  observe  where  they  rise  and  set  and  culminate. 
It  is  apparent,  then,  that  the  term  diurnal  arc  refers  only  to  the  interval 
during  which  a  celestial  object  is  above  the  horizon ;  and  this  inter- 
val of  time  (for  any  heavenly  body  except  the  sun)  may  elapse  partly 
during  actual  day  and  partly  during  night,  or  even  entirely  during  the 
night-time.  For  example,  note  the  rising  of  some  bright  star  near  the 
southeast.  How  slowly  it  appears  to  leave  the  horizon.  Notice  its  low 
elevation  when  it  reaches  the  meridian,  and  its  declining  arc  in  the 
southwest.  Evidently  its  diurnal  arc  is  very  short;  it  has  not. been 
above  the  horizon  more  than  seven  or  eight  hours  in  all. 

The  Diurnal  Motion  of  a  Star  Overhead.  —  Next  select 
a  bright  star  almost  overhead.  Early  in  September  even- 
ings in  the  United  States,  Vega  (Alpha  Lyrae)  will  be  in 
this  position.  As  it  descends  toward  the  west,  its  course 
will  seem  to  curve  rapidly  toward  the  north ;  and  as  it 
approaches  the  northwestern  horizon,  it  will  seem  to  go 
down  less  and  less  rapidly,  meanwhile  moving  more  and 
more  toward  the  north.  Finally,  it  will  disappear  only  a 


32  The  Language  of  Astronomy 

few  degrees  west  of  true  north.  In  making  this  circuit 
from  the  meridian  to  the  northern  horizon,  it  will  have 
consumed  perhaps  10  or  n  hours;  and  as  there  will  be 
a  similar  arc  of  10  or  n  hours  between  meridian  and 
eastern  horizon,  evidently  such  a  star's  diurnal  arc  may 
be  as  much  as  20  or  22  hours 'in  length. 

The  Diurnal  Motion  of  a  Circumpolar  Star.  —  Then 
choose  a  star  still  farther  north,  but  near  the  meridian, 
and  observe  its  motion  critically.  Very  noticeable  will  be 
the  fact  of  its  moving  away  from  the  meridian  less  rapidly 
than  the  star  just  observed.  It  will  not  go  nearly  so  far 
west,  and  after  about  six  hours  it  will  begin  to  return 
toward  the  north.  Then,  if  we  could  follow  it  into  the 
daylight,  six  hours  later  still,  or  about  12  hours  after  it 
was  first  observed,  it  would  be  seen  nearly  due  north,  and 
at  a  considerable  distance  above  the  horizon.  This  plane, 
in  fact,  it  will  never  have  reached.  It  will  then  continue 
to  move  backward  from  west  toward  east,  ascending  from 
the  horizon  at  first  very  slowly,  and  making  an  excursion 
as  far  east  of  the  meridian  as  it  was  observed  to  the  west. 
After  an  interval  of  24  hours  from  the  first  observation, 
this  star  will  be  seen  nearly  in  the  first  position,  just  like 
any  other  star,  having  described  an  entire  small  circle  of 
the  celestial  sphere ;  and  it  would  have  been  visible  all  the 
time  except  for  the  overpowering  brilliance  of  the  sun. 

The  Pole  Star.  —  If  we  select  a  star  yet  farther  north, 
we  shall  find  that  it  describes  an  even  smaller  circle  of  the 
celestial  sphere.  This  tentative  method  alone  would  enable 
us,  by  a  few  nights'  observations,  to  select  that  star  which 
describes  the  smallest  circle  of  all ;  the  bright  star  known 
as  [Stella]  Polaris,  or  the  pole  star.  Next  to  sun  and  moon 
the  most  important  object  in  the  heavens,  it  is  always  visi- 
ble in  all  places  in  the  United  States  when  the  sky  is  clear, 
not  only  by  night,  but  by  day  with  the  assistance  of  a 


How  to  Find  the  Pole  of  the  Heavens       33 

small  telescope.  The  center  of  the  very  small  circle  which 
Polaris  appears  to  describe  every  24  hours  is  the  north 
pole  of  the  heavens.  Also  the  diurnal  paths  of  all  other 
stars  are  central  about  it. 


Five-hour  Trails  of  Northern  Circumpolar  Stars  (photographed  by  Barnard) 

How  to  find  the  Pole  of  the  Heavens.  —  First  focus  the  camera  care- 
fully on  some  very  distant  object,  and  mount  it  in  the  meridian.  Secure 
it  firmly,  with  the  lens  directed  northward  and  upward  at  an  angle  of 
about  45°.  As  soon  as  the  stars  are  out,  and  it  has  become  quite  dark, 
take  off  the  cap  and  leave  the  plate  exposed  as  long  as  is  convenient, 
or  until  the  beginning  of  dawn.  Development  will  then  show  some- 
thing like  the  above,  a  series  of  concentric  arcs,  the  shortest  and 
brightest  of  which  will  be  that  of  Polaris.  Star  trails  will  be  broken 
lines,  if  clouds  temporarily  intervene.  At  the  center  of  all  these  curv- 
ing arcs  is  the  celestial  pole  itself,  always  situated  in  the  observer's  me- 
ridian ;  or  strictly  speaking,  the  meridian  is  the  vertical  circle  passing 
through  the  pole  of  the  heavens.  If  the  camera  is  pointed  near  the  celes- 
tial equator,  star  trails  will  be  straight  lines,  as  on  the  following  page. 
TODD'S  ASTRON.  —  3 


34  The  Language  of  Astronomy 

(B)  The  Equator  System.  —  The  north  pole  of  the 
heavens  is  a  fundamental  point  of  a  second  system  of 
planes  and  circles  of  the  celestial  sphere,  just  as  the  zenith 
is  the  primary  point  of  the  horizon  system.  Imagine 
this  horizon  system  of  planes  and  circles  —  horizon,  prime 
vertical,  meridian,  and  almucantar  —  to  be  outlined  in  a 
connected  skeleton  upon  the  vault  of  the  sky.  Also  think 
of  this  skeleton  system  as  pivoted  at  the  east  and  west 


One-hour  Trails  of  Stars  in  Orion's  Belt  (photographed  by  Barnard) 

points,  and  free  to  turn  about  them.  Then  move  the 
zenith  point  northward  along  the  meridian,  until  it  coin- 
cides with  the  north  pole.  The  south  point  of  the  horizon 
will  then  have  traveled  upward  along  the  meridian  by  an 
angle  equal  to  the  distance  of  the  zenith  from  the  north 
pole.  Also  the  north  point  of  the  horizon  will  have  been 
depressed  below  it  by  an  equal  arc.  In  this  novel  position 
the  circles  and  planes  of  the  celestial  sphere  need  defining 


The  Co  lures 


35 


anew.  What  was  the  zenith  is  now  the  north  pole  of  the 
heavens.  The  horizon  has  become  the  celestial  equator, 
every  point  of  which  is  distant  90°  from  the  celestial  pole, 
just  as  the  horizon  is  everywhere  90°  from  the  zenith.  What 
were  vertical  circles  now  converge  toward  the  poles,  the 
southern  one  of  which  is  depressed  below  the  south  horizon 
as  much  as  the  northern  one  is  elevated  above  it.  Instead 
of  vertical  circles  they  are  called,  in  this  position,  meridians 
of  the  celestial  sphere,  or  hour  circles.  They  correspond 
to,  and  are  planes -extended  from,  the  terrestrial  meridians 
of  geography.  Al- 
mucantars  in  system 
(A)  become  parallels 
of  declination  in  sys- 
tem (B). 

The  Colures. —  Evi- 
dently an  hour  circle 
may,  if  desired,  be 
drawn  through  any 
star  of  the  sky.  Two 
of  these  hour  circles 
at  right  angles  to 
each  other,  have  es- 
pecial names ;  they 
are  counterparts  of 
prime  vertical  and 
meridian  in  the  first 
or  horizon  system, 
and  are  called  the 
equinoctial  colure  and 
the  solstitial  colure. 

The  equator,  both  the  colures,  and  all  the  other  hour 
circles  have  nearly  constant  directions  and  fixed  positions 
among  the  stars,  just  as  the  prime  vertical  and  the  merid- 


Cnief  Circles  of  Equator  System  (B) 


36  The  Language  of  Astronomy 

ian  have  with  reference  to  the  landscape  at  a  particular 
place.  The  absolute  position  of  the  north  pole,  the 
celestial  equator,  and  its  colures  among  the  stars  can  be 
determined  at  any  time ;  and  the  astronomical  processes 
by  which  this  is  done  will  be  indicated  farther  on.  Equa- 
tor and  colures  should  be  concretely  illustrated  by  three 
hoops  secured  at  right  angles,  as  in  the  horizon  system. 

Equator  System  glides  over  Horizon  System.  —  It  has 
already  been  seen  that  the  stars  themselves,  by  the  diurnal 
motion,  cross  the  planes  and  circles  of  the  horizon  system 
at  a  great  variety  of  angles  and  velocities ;  evidently  then, 
as  the  circles  of  the  new  system  are  practically  fixed 
among  the  stars,  the  circles  of  this  equator  system  must 
be  imagined  as  all  the  time  gliding  over  and  across  those 
of  the  horizon  system.  Spherical  astronomy  is  a  branch 
of  the  science  dealing  very  largely  with  the  relations  of 
equator  and  horizon  systems ;  and  is  mostly  concerned 
with  the  angles  that  the  circles  of  the  horizon  system 
make  with  those  of  the  equator  system.  The  problems 
arising  are  mostly  solved  by  means  of  that  branch  of 
mathematics  called  spherical  trigonometry,  which  is  the 
science  of  ascertaining  all  the  different  parts  of  triangles 
described  on  the  sphere,  from  certain  parts  that  have  been 
measured  by  instruments. 

(C)  The  Ecliptic  System.  —  A  third  system  of  planes 
and  circles  of  the  celestial  sphere,  much  used  in  astronomy, 
may  best  be  defined  and  illustrated  here,  because  it  follows 
naturally  and  readily  from  the  horizon  system  and  the 
equator  system.  An  idea  of  its  relation  to  these  other 
systems  is  easily  obtained  on  recalling  the  way  in  which 
the  equator  system  was  derived  from  the  horizon  system 
-  by  pivoting  the  latter  at  the  east  and  west  points,  and 
turning  the  skeleton  horizon  system  about  these  pivots, 
until  the  zenith  became  the  north  pole  of  the  heavens. 


Equinoxes  and  Solstices 


37 


Now  in  a  precisely  similar  way,  imagine  the  equator 
system  pivoted  at  the  two  opposite  points  where  equator 
and  meridian  cross. 
Then  carry  the  north 
pole  toward  the  west 
23^°.  The  equator 
will  then  have  as- 
sumed a  position  in- 
clined by  an  angle  of 
23 J°  to  its  former 
position.  It  will,  in 
short,  have  become 
the  ecliptic ;  and  in 
this  novel  relation 
nearly  all  the  ele- 
ments of  the  celestial 
sphere  must  again 
be  denned.  A  third 
system  of  hoops 
should  be  arranged 
as  in  the  illustration. 
The  ecliptic,  as  we 
shall  see  farther  on, 
is  the  path  in  which 

the  sun  seems  to  travel  completely  round  the  sky  once 
every  year  —  a  motion  entirely  distinct  from  that  now 
under  consideration. 

Parallels  of  Latitude,  Equinoxes  and  Solstices.  —  What 
was  the  north  pole  of  the  heavens  becomes,  in  the  ecliptic 
system,  the  north  ecliptic  pole.  The  equator  itself,  as 
has  been  said,  is  now  the  ecliptic.  What  were  vertical 
circles  in  the  horizon  system,  and  hour  circles  in  the 
equator  system,  are  now  ecliptic  meridians.  As  almucan- 
tars  became  parallels  of  declination,  so  now  parallels  of 


Chief  Circles  of  Ecliptic  System  i.O 


38  The  Language  of  Astronomy 

declination  become  parallels  of  celestial  latitude.  Upper 
of  the  two  pivotal  points  upon  which  equator  turned 
about  meridian  is  called  the  Vernal  Equinox,  or  First  of 
Aries;  its  opposite  point,  180°  away,  the  Autumnal  Equi- 
nox. Or  the  equinoxes  are,  simply,  two  opposite  points  of 
the  celestial  sphere  where  equator  and  ecliptic  cross  each 
other.  The  word  equinox  signifies  equality  of  day  and 
night ;  and  these  points  have  this  name  because  when  the 
sun  is  exactly  at  either  of  them  (in  spring  and  autumn), 
it  rises  due  east  and  sets  due  west.  As  the  relations  in 
the  figure  opposite  show,  it  is  12  hours  above  the  horizon, 
making  the  day,  and  an  equal  interval  of  12  hours  be- 
low the  horizon.  Day  and  night  are  therefore  equal  in 
duration.  Passing  along  the  ecliptic  eastward  90°  from 
the  vernal  equinox,  a  point  is  reached  that  bears  the 
name  Summer  Solstice  (the  sun's  place  in  the  latter  part  of 
June).  Exactly  opposite  to  it  in  the  sky,  or  90°  beyond 
the  autumnal  equinox,  is  situated  the  Winter  Solstice  (the 
position  of  the  sun  just  before  Christmas). 

Ecliptic  System  glides  over  Horizon  System. — The  eclip- 
tic system  of  planes  and  circles  maintains  an  almost  in- 
variable relation  to  the  equator  system  and  to  the  fixed 
stars.  Therefore  it  also  must  glide  over  the  seemingly 
stationary  circles  of  the  horizon  system,  in  much  the  same 
manner  that  the  planes  and  circles  of  the  equator  system  do. 
In  consequence,  however,  of  the  angle  of  23^-°  between 
equator  and  ecliptic  the  constantly  varying  relations  of 
the  ecliptic  system  to  the  horizon  system  will  be  more 
intricate  than  those  of  the  equator  system  to  the  horizon 
system.  But  all  these  relations  are  readily  understood, 
and  may  be  completely  solved  by  the  processes  of  spheri- 
cal astronomy. 

The  relation  of  equator  to  ecliptic,  and  their  apparent  daily  motion 
through  the  sky,  may  be  well  illustrated  by  a  plain  model  like  the  one 


Ecliptic  System  over  Horizon  System         39 

here  shown  —  two  pasteboard  disks  cut  together  and  secured  to  an 
ordinary  thread-spool  slipped  on  a  lead  pencil  pointing  upward  to  the 
pole,  and  twirled  round  in  the  direction  of  the  arrows.  In  the  first 
place,  the  north  pole  of  the  ecliptic,  being  23^°  from  the  north  pole 
of  the  heavens,  is  always  distant  66}3  from  the  equator,  and  so  seems 
to  move  round  the  pole  once  every  day,  exactly  as  if  it  were  a  star  in 
that  position.  Everywhere  in  the  United  States  the  north  ecliptic  pole 


RIGHT 


Model  showing  Apparent  Motion  of  Equator  and  Ecliptic 

is  perpetually  above  the  horizon.  The  solstices,  being  points  23^°  from 
the  equator,  the  summer  solstice  north  of  it,  and  the  winter  solstice 
south,  they  also  seem  to  move  round  the  sky  obliquely  to  the  vertical 
circles  of  the  horizon  system.  As  the  axis  of  revolution  of  the  celestial 
sphere  passes  through  the  north  and  south  poles  of  the  equator  system, 
the  equator  revolves  round  in  its  own  plane,  like  a  pulley  on  a  shaft,  and 
is  always  parallel  to  itself.  Evidently,  then,  the  ecliptic  must  partake 
of  a  wobbling  motion  because  of  its  constant  inclination  of  23^°  to  that 
seemingly  stationary  circle  among  the  stars,  the  celestial  equator.  These 
three  systems  of  circles  —  (A)  the  horizon  system,  (/>)  the  equator  system, 
(C)  the  ecliptic  system  —  comprise  all  that  are  in  general  use  by  the 
astronomers  of  the  present  day. 


4o 


The  Language  of  Astronomy 


Usual  Astronomical  Symbols.  —  There  is  a  variety  of 
symbols  in  common  use  for  expressing  in  abbreviated  form 
the  names  of  sun,  moon,  and  planets,  their  location  in  the 
sky,  the  signs  of  the  zodiac,  and  so  on.  Some  of  them  are 
frequently  employed  in  other  sciences  with  differing  signi- 
fications, but  their  astronomical  meanings  are  as  follows  :  — 


0  =  the  sun. 

([  =  the  moon. 

•  =  the  new  moon. 

O  =  the  full  moon. 

o*  =  conjunction,  or  the  same  in  }    . 

D  =  quadrature,  or  differing  90"  in     elt.hf  longltude  or 

<?  =  opposition,'  or  differing  1 80'  in  J    r^ht  ascenslon- 

&  =  the  ascending  node. 


£  =  Mercury. 
9  =  Venus. 
®  =  the  earth. 
$  =  Mars. 
y.  =  Jupiter. 
Jj  =  Saturn. 
§  =  Uranus, 
tp  —  Neptune. 


And  for  the  signs  of  the  zodiac  (not  the  constellations  of  the  same 
name),  the  following:  — 


(I) 
(II) 
(III) 

(IV) 

(V) 

(VI) 


<¥>  Aries 
&  Taurus 
EC  Gemini 

95  Cancer 
SI  Leo  . 
"X  Virgo 


Spring 
signs. 


Summer 
signs. 


(VII) 

(VIII) 

(IX) 

(X) 

(XI) 

(XII) 


it  Libra 
TT\,  Scorpio 
/  Sagittarius 

Y3  Capricornus  ] 


CJf  Aquarius 
X  Pisces 


Autumn 
signs. 

Winter 
signs. 


The  explanation  of  technical  terms  used  above  will  be  given  subse- 
quently in  appropriate  paragraphs. 

Expressing  Large  Numbers.  —  In  astronomy  there  is  frequent  oc- 
casion to  express  very  large  numbers,  because  our  earth  is  so  small  a 
part  of  the  universe  that  terrestrial  units  often  have  to  be  multiplied 
over  and  over  again,  in  order  to  represent  celestial  magnitudes.  In 
this  book,  and  in  accordance  with  American  usage  generally,  the 
French  system  of  enumeration  is  used.  From  one  million  upward,  it 
is  as  follows  :  — 

1,000,000  =  one  million         ] 


1,000,000,000  =  one  billion 
1.000,000,000,000  =  one  trillion 
1,000,000,000,000,000  =  one  quadrillion 
etc.  etc. 


The  usual 

or 
French  system. 


through   quintillions,  sextillions,  and  so  on;    the  Latin  terms  being 
employed,  and  each  order  being  1000  times  that  next  preceding  it.     It 


Directions  in  the  Heavens  41 

is  necessary,  however,  to  note  that  in  works  on  astronomy  published  in 
England,  and  now  widely  circulated  in  America,  the  English  system  of 
enumeration  is  always  employed.  The  terms  billion,  trillion,  quadrillion, 
and  so  on  are  used,  but  with  entirely  different  signification :  each  is  one 
million,  instead  of  1000,  times  the  one  next  preceding  it.  So  that 

1,000,000  =  one  million  (English) 

=  one  million  (French) 

1,000,000,000,000  =  one  billion  (English) 

=  one  trillion  (French) 

1,000,000,000,000,000,000  =  one  trillion  (English) 

=  one  quintillion  (French) 

Also,  very  large  numbers  are  often  expressed   by  an  abridged  or 
algebraic  notation,  in  which  there  is  no  ambiguity. 

Thus,        3  x  io9   =         3,000,000,000  =  three  billions  (French) 
6  x  io12  =  6,000,000,000,000  =  six  billions  (English) 

=  six  trillions  (French) 

The  small  figure  above  the  io  is  called  an  exponent,  and  indicates 
the  number  of  times  that  io  is  taken  as  a  multiplier. 

East  and  West,   North  and  South,   in  the  Heavens.  - 

Ordinary  and  restricted  use  of  these  terms,  as  adopted 
from  geography,  has  already  been  defined:  north  and  south 
state  the  direction  of  the  true  meridian  ;  an  east  and  west 
line  is  horizontal  and  at  right  angles  to  a  north  and  south 
one.  This  use  of  these  terms  is  wholly  confined  to  the 
planes  and  circles  of  system  (A),  whose  fundamental  plane 
is  the  horizon.  When,  however,  we  pass  to  systems  (B) 
and  (C),  the  meaning  of  the  terms  east  and  west,  north  and 
south,  changes  also,  to  correspond  with  their  fundamental 
planes.  As  related  to  these  systems,  then,  we  must  define 
north,  south,  east,  and  west  anew.  North  is  the  direction 
from  any  celestial  body  toward  the  north  pole  of  the 
heavens ;  it  is  a  constantly  curving  direction  along  the 
hour  circle  passing  through  that  body.  Similarly,  south 
is  the  opposite  direction,  along  the  same  hour  circle, 
toward  the  south  pole.  Immediately  underneath  the 
pole,  south,  in  system  (/?),  means  toward  the  north  point 


42  The  Language  of  Astronomy 

of  the  horizon.  East  and  west  lie  along  equator  and 
parallels  of  declination,  in  curving  directions  on  the  celes- 
tial sphere.  When  facing  toward  the  south,  east  is  the 
direction  toward  the  left,  or  counter-clockwise  around 
equator  and  parallels.  The  farther  north  or  south  a 
star  is,  the  smaller  its  parallel,  and  the  more  rapid  the 
curvature  of  the  direction  east  and  west  from  it.  Also 
the  terms  east  and  west,  north  and  south,  are  often  used 
with  reference  to  the  planes  and  circles  of  system  (C); 
north  and  south  then  lie  along  ecliptic  meridians,  and 
east  and  west  are  at  right  angles  to  these  meridians,  in 
the  curving  direction  of  ecliptic  and  parallels  of  celestial 
latitude.  East  is  counter-clockwise,  as  in  system  (B\  and 
north  is  toward  the  north  pole  of  the  ecliptic. 

We  are  now  prepared  to  consider  the  relations  of  these 
three  systems  to  the  work  of  the  practical  astronomer,  to 
study  the  terminology  of  each,  and  to  trace  their  points  of 
geometric  likeness  philosophically. 


CHAPTER   III 


THE   PHILOSOPHY   OF  THE   CELESTIAL   SPHERE 

AS  the  conception  of  the  celestial  sphere  is  now  under- 
stood, we  next  give  the  reasons  underlying  the  differ- 
ent systems  already  explained.  These  reasons  are 
fundamental,  having  their  origin  in  the  principles  of  geome- 
try itself.  They  have  been  known  and  accepted  since  the 
days  of  Euclid  (B.C.  280),  who  first  gave  a  rational  explana- 
tion of  all  those  ordinary  phenomena  of  the  celestial  sphere 
that  the  ancients 
were  able  to  ob- 
serve. Practical 
astronomy  is  the 
science  of  accurate 
observation  and 
calculation  of  the 
positions  of  the 
heavenly  bodies. 
In  order  that  it 
should  advance 
from  a  rudimen- 
tary beginning,  the 
observations,  as 

All  Circles  are  divided  into  360  Degrees 

well  as  the  mathe- 
matical   processes   by  which   they   were   calculated,    had 
to  be  accurate.      Precise    observation   was    possible   only 
when    the    heavenly   bodies   could    be   referred   to    some 
established    point,    or    circle,    or    plane.       Naturally   the 

43 


0°  360° 


t 


44  Philosophy  of  the  Celestial  Sphere 

horizon  was  the  first  plane  of  reference,  because  the 
rising  and  setting  of  sun  and  moon  and  the  brighter  stars 
could  be  watched  quite  definitely.  This  fact  explains  the 
origin  of  the  fundamental  plane  of  the  horizon  system. 
Its  related  points,  circles,  and  planes  came  naturally  and 
necessarily  from  the  principles  of  geometry. 

The  Measure  of  Angles.  —  In  astronomical  measure- 
ments, circles  of  all  possible  sizes  are  dealt  with ;  and 
every  circle  regardless  of  its  size  is  divided  into  360°. 
The  degree  is  a  unit  of  angular  measure,  not  of  length  ; 
and  its  value  as  described  on  a  circular  arc  varies  uniformly 
with  the  size  of  the  circle.  In  concentric  circles,  for  ex- 
ample, the  number  of  degrees  included  between  any  two 
radii,  as  illustrated  on  the  preceding  page,  is  the  same 
in  all  circles.  Every  degree  is  divided  into  60',  and  every 
minute  into  60".  Do  not  confuse  with  the  same  symbols, 
^>ften  used  to  designate  feet  and  inches. 

Light  moves  in  Straight  Lines. —  All  astronomy  is  based 
on  the  truth  of  the  proposition  that,  in  a  homogeneous 
medium  like  the  ether,  a  weightless  substance  filling  space, 
light  moves  in  straight  lines.  The  physicist  demonstrates 
this  from  the  wave  theory  of  the  motion  of  light. 

The  nature  of  a  homogeneous  medium  may  be  illustrated  by  contrast 
with  one  that  is  not  so.  Look  out  of  the  window  at  objects  seen  just 
above  the  top  of  a  heated  radiator.  They  appear  to  be  quivering  and 
indistinct.  We  know  that  such  objects — buildings,  signs,  trees  —  are 
really  not  distorted,  as  they  seem  to  be ;  and  we  refer  this  temporary 
appearance  to  its  true  cause  —  the  irregular  expansion  of  the  air  sur- 
rounding the  radiator.  A  portion  of  the  medium,  then,  through  which 
the  light  has  parsed,  from  the  objects  outside  to  the  eye,  is  not  homo- 
geneous ;  and  we  know  that  if  the  radiator  and  the  air  round  it  were 
of  the  same  temperature,  there  would  be  no  such  blending  and  scattering 
of  the  rays.  The  light  passing  over  a  heated  chimney,  the  air  above  an 
asphalt  walk  on  which  the  sun  is  shining,  a  flagstaff  seemingly  cut  in 
two  on  a  sunny  day  (when  the  eye  is  placed  close  to  it  and  directed 
upward),  — these  and  many  other  simple  phenomena  have  a  like  origin. 
That  violent  twinkling  of  the  stars  which  adds  so  much  to  the  beauty 


Angles  and  Distances 


45 


of  a  winter  night  is  due  in  large  part  to  a  vigorous  commingling  of 
warm  air  with  cold,  causing  departure  of  the  light-bearing  medium  from 
a  perfectly  homogeneous  structure.  On  such  nights  the  telescope 
cannot  greatly  assist  the  eye  in  astronomical  observations. 

Angles  and  Distances.  —  As  light  moves  in  straight  lines, 
the  angle  which  a  body  seems  to  fill,  or  subtend,  is  wholly 
dependent  upon  its  distance  from  the  eye.  The  more  remote 


The  Nearer  the  Track,  the  Broader  it  seems  ^Instantaneous  Photograph  by  Trowbridge) 

a  given  object  is,  the  smaller  the  angle  it  subtends,  and  the 
nearer  it  is,  the  greater  this  angle.  We  do  not  always  think 
of  this  when  crossing  a  straight  stretch  of  railway  track, 
although  we  know  that  the  rails  are  everywhere  the  same 
distance  apart.  But  the  camera,  by  projecting  all  objects 
on  a  plane  surface  regardless  of  their  distance,  brings  out 
prominently  the  great  difference  in  the  angular  breadth 
of  the  track  near  by  and  far  away,  so  well  shown  in  the 
picture.  By  trial  we  readily  verify  the  following  law :  - 


46  Philosophy  of  the  Celestial  Sphere 


Angles  subtended  by  a  given  object  are  inversely  proportional 
to  the  distances  at  which  it  is  placed.  Consequently  a 
number  of  bodies  of  various  sizes  —  the  silver  dollar,  the 
saucer,  and  the  bicycle  wheel,  as  shown  in  the  illustra- 
tion —  may  all  subtend  exactly  the  same  angle,  provided 
they  are  placed  at  suitable  distances.  Obviously,  then,  it 
is  very  indefinite  to  say  that  the  moon  looks  as  big  as  a 


If  Bodies  fill  the  Same  Angle,  their  Size  is  Proportional  to  their  Distance 

dinner  plate  or  a  cart  wheel,  or  anything  else,  unless  at  the 
same  time  it  is  stated  how  far  from  the  eye  the  dinner 
plate  or  cart  wheel  or  other  object  is  supposed  to  be. 

Moon  and  the  Radian  are  Standards.  —  Observation 
shows  that  the  moon  actually  subtends  an  angle  of  about 
one  half  a  degree ;  and  it  has  been  demonstrated  by  geom- 
etry that  a  sphere  whose  distance  is 

206,000  j  r  i" 

3,400  [  times  its  diameter  just  fills  an  angle  of  |  i' 
57  J  I  '° 

These  numbers  are  obtained  accurately  as  follows:-  Recalling  the 
rule  of  mensuration  concerning  the  circle,  whose  radius  is  r,  its  circum- 
ference, or  360°  =  2-n-r,  TT  being  the  familiar  3.14159,  or  3}.  But  as 

2irr  =  360°  =  21,600'  =  1,296,000", 
'  =  57i°  =    3,438'=     206,265". 

The  angle  r  is  a  convenient  unit  of  angular  measure.  As  it  is  the 
arc  measured  on  the  circumference  of  any  circle  by  bending  the  radius 
round  it,  this  angle  is  often  called  the  radian. 


Altitude  and  Azimuth 

So  that  if  the  distance  of  an  object  from  the  eye  is 
equal  to  1 1 5  times  its  diameter,  it  will  subtend  the  same 
angle  that  the  moon  does,  and  so  will  appear  to  be  of 
the  same  size  as  the  moon.  The  eye  is  often  deceived  in 
the  distance  and  size  of  objects,  generally  placing  them 
much  nearer  than  they  should  be.  This  experiment  is 
very  easily  tried :  an  ordinary  copper  cent,  in  order  to 
fill  the  same  angle  as  the  moon  should  be  placed  at  a 
distance  of  about  seven  feet ;  while  a  silver  dollar  should 
be  nearly  14^  feet  away.  The  moon,  then,  always  filling 
nearly  the  same  angle  of  |-°,  is  an  excellent  standard  of 
angular  value ;  a  small  unit  of  arc  measure.  To  express 
the  apparent  distance  of  a  planet,  for  example,  from  a  star 
alongside  it,  estimate  how  many  times  the  moon's  disk 
could  be  contained  between  the  two  objects;  then  half 
this  number  will  express  the  distance  roughly  in  degrees. 
Though  the  result  may  be  somewhat  erroneous,  the  prin- 
ciple is  correct. 

Altitude  and  Azimuth. — -Altitude  is  the  angular  dis- 
tance of  a  body  above  the  horizon ;  and  it  is  measured 


Stars  of  Equal  Altitude 


Stars  of  Equal  Azimuth 


along  the  arc  of  the  vertical  circle  passing  through  the 
body.  Evidently  the  altitude  of  the  zenith  is  90°,  and 
this  is  the  maximum  altitude  possible.  Oftentimes  the 


48  Philosophy  of  the  Celestial  Sphere 

term  zenith  distance  is  used ;  it  is  always  equal  to  the 
difference  between  90°  and  the  altitude.  But  in  order  to 
fix  the  position  of  a  body  in  the  sky,  it  is  not  sufficient 
to  give  its  altitude  alone.  That  simply  tells  us  that  it 
is  to  be  found  somewhere  in  a  particular  small  circle,  or 
almucantar ;  but  as  it  may  be  anywhere  in  that  circle,  a 
second  element,  called  azimuth,  becomes  necessary.  This 
tells  us  in  what  part  of  the  almucantar  the  star  is  to  be 
found.  Azimuth  is  the  angular  distance  of  a  body  from 
the  meridian ;  and  it  is  measured  along  the  horizon  from 
the  south  point  clockwise  (  that  is,  in  the  direction  of  mo- 
tion of  the  hands  of  a  clock),  or  through  the  points  west, 
north,  east,  to  the  foot  of  the  star's  vertical  circle.  Azi- 
muth, then,  may  evidently  be  as  great  as  360°.  The  position 
of  a  star  in  the  northwest,  and  40°  from  the  zenith,  would 
be  recorded  as  follows:  altitude  50°,  azimuth  135°.  One 
at  10°  from  the  zenith,  but  in  the  southeast,  would  be : 
altitude  80°,  azimuth  315°.  The  figures  (page  47)  make 
it  clear  that  many  stars  may  have  equal  altitudes,  although 
their  azimuths  all  differ;  while  yet  others,  if  located  on 
the  same  vertical  circle,  may  have  equal  azimuths,  although 
their  altitudes  range  between  o°  and  90°. 

A  Simple  Altazimuth  Instrument.  —  This  simple  and  readily  built 
instrument  is  all  that  is  needed  to  find  altitudes  and  azimuths.  Of 
course  the  measures  will  be  made  roughly,  but  the  principles  are  per- 
fectly correct.  The  illustration  shows  plainly  the  essentials  of  construc- 
tion. From  the  corners  of  a  firm  board  base  about  two  feet  square,  let 
four  braces  converge,  to  hold  an  upright  bearing,  just  below  the  azimuth 
circle.  Through  this  bearing  run  an  upright  pole  or  straight  piece  of 
gas  pipe,  letting  it  rest  in  a  socket  on  the  base,  in  which  it  is  free  to 
turn  round.  A  broom  handle  run  through  two  holes  bored  in  the  mid- 
dle of  two  opposite  sides  of  a  packing  box  will  do  very  well,  in  default 
of  anything  better.  Just  above  the  azimuth  circle  attach  to  the  upright 
axis  a  collar  with  a  pointer  equal  in  length  to  the  radius  of  the  azimuth 
circle.  It  is  more  convenient  if  this  collar  is  fastened  by  a  set  screw. 
The  circle  is  made  of  board,  to  which  is  glued  a  circle  of  paper  or 


Use  of  the  Altazimuth 


49 


thin  card,  divided  in  degrees,  beginning  with  o°  at  S,  and  running 
through  90°  at  W,  180°  at  N,  270'  at  E,  and  so  on.  After  dividing 
and  numbering,  the  circle  may  be  covered  with  two  or  three  coats  of 
thin  shellac,  in  order  to  preserve 
it.  Attach  to  the  top  of  the 
vertical  axis  a  second  circle,  the 
altitude  circle,  divided  through 
its  upper  half,  from  o°  on  each 
side  up  to  90°,  or  the  zenith. 
Through  the  center  of  the  altitude 
circle  run  a  horizontal  bearing; 
it  is  better  if  large,  say  \  inch  or 
more,  because  the  index  arm 
attached  to  it  will  then  turn  more 
evenly,  and  stop  at  any  required 
position  more  sharply.  In  line 
with  the  index  point  and  the  cen- 
ter of  the  bearing,  attach  two 
sights  near  the  ends  of  the  arm. 
Essentially  the  altazimuth  instru- 
ment is  then  complete.  Sights 
for  use  upon  stars  with  the  naked 
eye  should  be  of  about  this  size 

and  construction  : 

The  aperture  of 
Model  Sight  about  =  inch  does 
not  diminish  the  star's  light,  and 
the  small  cross  threads  or  wires 
give  the  means  of  fairly  accurate 
observation. 

Use  of  the  Altazimuth.  —  To 
use  it,  level  the  azimuth  circle, 
and  bring  the  line  through  N 
and  S  to  coincide  with  the  merid- 
ian, already  found.  See  that  the 
line  of  zeros  of  the  altitude  circle 
is,  as  nearly  as  may  be,  at  right 
angles  to  the  vertical  axis. 
Point  the  sights  in  the  line  of 

the  meridian,  and  while  looking  northward,  damp  the  azimuth  pointer 
exactly  at  180°,  by  means  of  its  collar.  The  instrument  is  then  ready 
for  use ;  and  on  pointing  it  at  any  celestial  body,  its  altitude  and 
azimuth  at  the  time  of  observation  may  be  read  directly  at  the  ends  of 
the  pointers  of  the  two  circles.  If  the  instrument  has  been  made  and 
TODD'S  ASTRON.  —  4 


Model  of  the  Altazimuth 


50  Philosophy  of  the  Celestial  Sphere 

adjusted  with  even  moderate  care,  its  readings  will  pretty  surely  be 
within  one  degree  of  the  truth  ;  and  for  practicing  the  eye  in  roughly 
estimating  altitudes  and  azimuths  at  a  glance,  nothing  could  be  better. 
Also  take  the  altitude  of  the  sun  and  stars  when  on  the  meridian  and 
the  prime  vertical.  To  observe  the  sun  most  conveniently,  let  its  rays 
pass  through  a  pin  hole  at  the  upper  end  of  the  index,  or  pointer,  and 
fall  upon  a  card  at  the  lower  end  with  a  cross  marked  upon  it;  care 
being  taken  that  the  line  of  the  pin  hole  and  the  cross  is  parallel  to  the 
line  of  sights. 

Origin  of  the  Equator  System.  —  The  motion  of  the 
celestial  sphere  is  continually  changing  the  altitude  and 
azimuth  of  a  star.  Consequently  the  horizon  and  its  con- 
nected circles  are  a  very  inconvenient  system  of  noting  the 
positions  of  stars  with  reference  to  each  other ;  even  the 
ancients  had  observed  that  these  bodies  did  not  seem  to 
move  at  all  among  themselves  from  age  to  age.  It  was 
natural  and  necessary  therefore  to  devise  a  system  of  co- 
ordinates, as  it  is  called,  in  which  the  stars  should  have 
their  positions  fixed,  or  nearly  so.  From  the  time  of 
Euclid,  at  least,  a  philosopher  here  and  there  was  satisfied 
that  the  earth  is  round,  that  it  turns  on  its  axis,  and  that 
the  axis  points  in  a  nearly  constant  direction  among  the 
stars.  Readily  enough,  then,  arose  the  second,  or  equator 
system  of  elements  of  the  celestial  sphere ;  the  upper  end 
of  the  earth's  axis  prolonged  to  the  stars  gave  the  primal 
point  of  the  system  —  the  north  pole  of  the  heavens. 
Everywhere  90°  from  it  is  the  great  circle  girdling  the  sky, 
in  the  plane  of  the  earth's  equator  extended,  and  called 
therefrom  the  celestial  equator. 

Declination.  — This  plane  or  circle  (often  termed  the  equi- 
noctial, but  generally  called  the  eqtiator  simply),  becomes 
the  fundamental  reference  plane  of  the  equator  system 
(B\  It  sustains  exactly  the  relation  to  the  equator  system 
that  the  horizon  has  to  the  horizon  system  (A).  And, 
similarly,  two  terms  are  necessary  to  fix  the  position  of  a 


Right  Ascension  5 1 

star  relatively  to  the  equator.  First,  the  declination,  which 
is  the  counterpart  of  altitude  in  system  (A).  The  declina- 
tion of  a  body  is  its  angular  distance  from  the  equator ;  and 
it  is  measured  north  or  south  from  that  plane,  along  the 
hour  circle  passing  through  the  body.  If  the  star  is  north 
of  the  equator,  it  is  said  to  be  in  north  or  plus  declination; 
if  south,  then  in  minus  or  south  declination.  Evidently, 
stars  north  of  the  equator  may  have  any  possible  declina- 
tion up  to  plus  90°,  the  position  of  the  north  pole  ;  and  stars 
south  of  the  equator  cannot  exceed  a  declination  of  minus 
90°.  The  symbol  for  declination  is  decl,  or  simply  S  (the 
small  Greek  letter  delta).  Sometimes  the  term  north  polar 
distance  is  substituted  for  declination ;  and  it  is  counted 
along  the  star's  hour  circle  southward,  from  the  north  pole, 
right  through  the  equator  if  necessary.  North  polar  dis- 
tance cannot  exceed  180°,  the  position  of  the  south  pole  of 
the  heavens.  For  example,  the  north  polar  distance  of  a 
star  in  declination  +20°  is  70°;  and  if  the  declination  is 
—  22°,  the  north  polar  distance  is  112°. 

Right  Ascension.  —  Recalling  again  the  terms  and  circles 
of  the  horizon  system,  it  is  apparent  that  declination 
alone  cannot  fix  a  star's  position  on  the  celestial  sphere 
any  more  than  mere  altitude  can.  It  would  be  like  try- 
ing to  tell  exactly  where  a  place  on  the  earth  is  by  giving  its 
latitude  only ;  the  longitude,  or  angular  distance  on  the 
earth's  equator  from  a  prime  meridian  must  be  given  also. 
So  the  companion  term  for  declination  is  right  ascension  ; 
and  it  is  the  counterpart  of  azimuth  in  the  horizon  sys- 
tem (A).  But  note  two  points  of  difference.  The  right 
ascension  of  a  body  is  its  angular  distance  from  the  vernal 
equinox  (a  point  in  the  equator  whose  definition  has  already 
been  given  on  page  38).  Right  ascension  is  measured 
eastward,  or  counter-clockwise,  along  the  equator,  to  the 
hour  circle,  passing  through  the  body.  It  may  be  meas- 


52  Philosophy  of  the  Celestial  Sphere 

ured  all  the  way  round  the  heavens,  and  therefore  may 
be  as  great  as  360°.  But  as  a  matter  of  convenience 
purely,  right  ascension  is  generally  denoted  in  hours,  not 
degrees  (figure  on  page  39).  As  24  hours  comprise  the 
entire  round  of  the  sky,  and  360°  do  the  same,  one  may  be 
substituted  for  the  other.  Each  hour,  then,  will  comprise 
as  many  degrees  as  24  is  contained  times  in  360;  that 


Stars  of  Equal  Declination 


Stars  of  Equal  Right  Ascension 


is,  15.  Also  hours  are  divided  into  minutes  and  minutes 
sub-divided  into  seconds  of  time,  just  as  degrees  are,  into 
minutes  and  seconds  of  arc.  So  that  we  have  :  — 

ih.  =15°  1  f  i°  =  4m. 

i  m.  =  15'    [     and     j   i'   =45. 


i  s.    =  15"  J  I  i"  =0.06675. 

These  are  relations'  constantly  required  in  astronomy. 
Usual  symbols  for  right  ascension  are  R.  A.,  or  IR,  or 
simply  a  (the  small  Greek  letter  alpha),  standing  for 
ascensio  recta.  The  figures  make  it  clear  that  stars  may 
have  equal  right  ascension,  although  their  declinations 
differ  widely,  and  vice  versa. 

The  Equatorial  Telescope.  —  Just  as  the  altazimuth  is 
an  instrument  whose  motions  correspond  to  the  horizon 
system,  so  the  motions  of  the  equatorial  telescope  corre- 
spond to  the  equator  system.  This  instrument,  generally 


The  Eqiiatorial  Telescope 


53 


called  merely  the  cqtiatorial,  is  a  form  of  mounting  which 
enables  a  star  to  be  followed  in  its  diurnal  motion  by  turn- 
ing the  telescope  on  only  one  axis. 

This  axis  is  always  parallel  to  the  axis  of  the  earth,  and  is  called  the 
polar  axis.  As  it  must  point  toward  the  north  pole  of  the  heavens,  the 
polar  axis  will 
stand  at  about 
the  angle  shown 
in  the  picture, 
for  all  places  in 
the  United 
States.  The 
simplest  way  to 
understand  an 
equatorial  is  to 
regard  it  as  an 
altazimuth  with 
its  principal  or 
vertical  axis 
tilted  northward 
until  it  points 
to  the  pole. 
The  azimuth  cir- 
cle then  becomes 
the//0«r  «'r£/*  of 
the  equatorial  ; 
the  horizontal 
axis  becomes  the 
decimation  axis 
of  the  equato- 
rial ;  and  the 
circle  attached 
to  it  is  called  the 
declination  circle 
(the  counterpart 

of    the     altitude 

circle      in     the 

altazimuth).  At  one  end  of  the  declination  axis  and  at  right  angles  to 
it  the  telescope  tube  is  attached,  as  shown.  The  model  in  the  illustra- 
tion may  be  constructed  by  any  clever  boy.  The  axes  are  pine  rods 
running  through  wooden  bearings,  and  it  is  well  to  soak  them  with  hot 
paraffin.  The  telescope  tube  is  a  large  pasteboard  roll. 


Model  of  the  Equatorial  Telescope 


54  Philosophy  of  the  Celestial  Sphere 


How  to  adjust  and  use  this  Equatorial.  —  Having  already  found 
direction  of  the  meridian,  the  polar  axis  must  be  brought  into  its  plane, 
and  the  north  end  of  this  axis  elevated  to  an  angle  equal  to  the  latitude. 
This  can  be  taken  accurately  enough  from  any  map  of  the  United  States. 

Draw  a  line  on  the  out- 
side of  the  bearing  of 
the  polar  axis  parallel 
to  the  axis  itself;  and 
across  this  line,  at  an 
angle  equal  to  the  lati- 
tude (laid  off  with  a 
protractor),  draw  an- 
other line  which  will  be 
nearly  horizontal.  The 
adjustment  is  completed 
by  means  of  an  ordi- 
nary artisan's  level, 
placed  alongside  this 
second  line.  Take  out 
the  object  glass  and  eye- 
piece, and  point  the  tele- 
scope at  the  zenith,  as 
nearly  as  the  eye  can 
judge.  Then  hang  a 
plumb-line  through  the 
tube,  suspending  it  from 
the  center  of  the  upper 
end,  and  continuing  to 
adjust  the  tube  till  the 
line  hangs  centrally 
through  it.  While  the 
tube  remains  fixed  in 
this  position,  set  the 
hour  circle  to  read  zero, 
and  the  declination  circle 
to  a  number  of  degrees 
equal  to  the  latitude. 
The  model  equatorial  is 
then  readv  to  use.  Dec- 


1 0-Inch  Equatorial  (Warner  &  Swasey 


linations  can  be  read  from  the  declination  circle  directly,  bringing 
any  heavenly  body  into  the  center  of  the  field  of  view.  And  right 
ascensions  can  be  found  when  the  hour  angle  of  the  vernal  equinox 
is  known.  A  method  of  finding  this  will  be  given  in  the  next  chapter 
(p.  66).  Distinguish  between  the  double  and  differing  significations 


Celestial  Latitude 


55 


of  the  term  hour  circle :  when  the  equatorial  is  adjusted,  its  hour  circle, 
being  parallel  to  the  terrestrial  equator,  is  therefore  at  right  angles  to 
the  hour  circles  of  the  celestial  sphere. 

Telescopes  as  mounted  in  Observatories.  —  Nearly  all  the  telescopes 
in  observatories  are  mounted  equatorially.  The  cardinal  principles 
of  these  mountings  are  similar  to  those  of  the  model  already  given. 
An  equatorial  telescope  is  shown  in  the  illustration  opposite.  The 
small  tube  at  the  lower  end  of  the  large  one  and  parallel  to  it  is  a 
short  telescope  called  the  '  finder,1  because  it  has  a  large  field  of  view, 
and  is  used  as  a  convenience  in  finding  objects  and  bringing  the  large 
telescope  to  bear  upon  them.  Iron  piers,  nearly  cylindrical  in  the  best 
mountings,  but  often  rectangular,  are  now  generally  employed  in  sup- 
porting the  axes  of  telescopes.  An  hour  circle  is  sometimes  attached 
to  the  upper  end  of  the  polar  axis,  as  shown ;  and  geared  to  the  out- 
side of  this  circle  is  a  screw  or  worm,  turned  by  clockwork  (underneath 
in  the  middle  of  the  pier) .  The  clock  is  so  regulated  as  to  turn  the 
polar  axis  once  completely  round  from  east  toward  west  in  the  same 
period  that  the  earth  turns  once  completely  round  on  its  axis  from 
west  toward  east.  When  a  star  has  been  placed  in  the  field  of  view, 
and  the  axis  clamped,  the  clock  maintains  it  there  without  readjusting, 
as  long  as  the  observer  may  care  to  watch.  Each  axis  of  a  large 
equatorial  is  provided  with  a  mechanical  convenience  called  a  '  slow 
motion,1  one  for  right  ascension  and  one  for  declination.  These 
devices  are  operated  by  handles  (at  the  right  of  the  tube),  which  can 
be  turned  by  the  observer  while  looking  through  the  eyepiece;  and 
they  enable  him  to  move  an  object  slowly  from  one  part  of  the  field 
of  view  to  another,  as  required. 


Celestial  Latitude.  —  The  third  system  of  coordinates  of 
the  celestial  sphere — (C)  the  ecliptic  system — is  founded 
on  the  path  which  the  sun  seems  to  travel  among  the  stars, 
going  once  around  the  entire  heavens  every  year.  In  fact, 
the  ecliptic  is  usually  defined  as  the  apparent  annual  path 
of  the  sun's  center.  This  path  is  a  great  circle  of  the 
celestial  sphere.  And  as  it  always  remains  constant  in 
position,  relatively  to  the  fixed  stars,  its  convenience  as  a 
fundamental  plane  of  reference  is  easy  to  see.  The  name 
ecliptic  is  applied,  because  eclipses  of  sun  and  moon  are 
possible  only  when  our  satellite  is  in  or  near  this  path. 
Upon  the  ecliptic  as  a  fundamental  plane  is  based  a  sys- 


56  Philosophy  of  the  Celestial  Sphere 

tern  of  coordinates,  precisely  as  in  the  equator  system 
Celestial  latitude,  or  a  star's  latitude  merely,  is  its  angular 
distance  from  the  ecliptic ;  and  it  is  measured  north  or 
south  from  that  plane,  along  the  ecliptic  meridian  passing 
through  the  star.  Latitude  is  the  counterpart  of  altitude 
in  the  horizon  system,  and  of  declination  in  the  equator 
system.  If  the  star  is  north  of  the  ecliptic,  it  is  said  to 
be  in  north  or  phis  latitude;  if  south,  then  in  minus  or  south 
latitude.  No  star  can  exceed  ±  90°  in  latitude.  As  the 
center  of  the  sun  travels  almost  exactly  along  the  ecliptic, 
year  in  and  year  out,  its  latitude  is  always  practically  zero. 
The  symbol  for  latitude  is  /3  (the  small  Greek  letter  beta). 
Sometimes  the  term  ecliptic  north  polar  distance  is  conven- 
ient ;  it  is  measured  southward  along  the  ecliptic  meridian 
passing  through  the  star.  It  is  independent  of  the  ecliptic 
itself,  and  may  have  any  value  from  o°  to  180°,  according 
to  the  star's  place  in  the  heavens.  A  star  whose  latitude 
is  —  38°  is  located  in  ecliptic  north  polar  distance  128°. 

Celestial  Longitude.  —  Celestial  longitude  is  the  term 
used  to  designate  the  angular  distance  of  a  star  from  the 
vernal  equinox,  measured  eastward  along  the  ecliptic  to 
that  ecliptic  meridian  which  passes  through  the  star.  It 
is  counted  in  degrees  from  o°  all  the  way  round  the 
heavens  to  360°  if  necessary.  By  drawing  a  figure  simi- 
lar to  that  on  -page  52,  and  replacing  the  celestial  pole 
by  the  pole  of  the  ecliptic,  it  becomes  clear  that  all  stars 
on  any  parallel  of  latitude  have  the  same  latitude,  no 
matter  what  their  longitudes  may  be  ;  and  that  all  stars 
on  any  half  meridian  of  longitude  included  between  the 
ecliptic  poles  must  have  the  same  longitude,  although  their 
latitudes  may  differ  widely.  As  the  equinoxes  mark  the 
intersection  of  equator  and  ecliptic,  they  must  both  be  in 
equator  and  ecliptic  alike.  On  the  ecliptic,  and  midway 
between  the  two  equinoxes,  are  two  points,  called  the 


Summary  and  Correlation  of  Terms         57 

solstices.  Hence  the  name  of  the  hour  circle,  or  colure 
which  passes  through  them  —  the  solstitial  colure.  At  the 
times  of  the  solstices,  the  sun's  declination  remains  for  a 
few  days  very  nearly  its  maximum,  or  23^°.  It  was  this 
apparent  standing  still  of  the  sun  with  reference  to  the 
equator  (north  of  the  equator  in  summer,  and  south  of  it 
in  winter)  which  gave  rise  to  the  name  solstice. 


In  observing  the  positions  of  the  heavenly  bodies  before  the  inven- 
tion of  clocks,  the  ancient  astronomers,  particularly  Tycho  Brahe,  used 
a  type  of  astronomical  instru- 
ment called  the  ecliptic  astro- 
labe, a  kind  of  armillary  sphere, 
in  which  the  longitude  and 
latitude  of  a  star  could  be  read 
at  once  from  the  circles.  But 
instruments  of  this  character 
are  now  entirely  out  of  date, 
only  a  few  being  preserved  in 
astronomical  museums,  the 
principal  one  of  which  is  at 
the  Paris  Observatory.  The 
astronomers  of  to-day  never 
determine  the  longitude  and 
latitude  of  a  body  by  direct 
observation,  but  always  by 
mathematical  calculation  from 
the  right  ascension  and  decli- 
nation ;  because  the  longitude 
and  latitude  can  be  obtained  in 
this  way  with  the  highest  accu- 


racy. 


The  Ecliptic  Astrolabe 


Summary  and  Correlation  of  Terms.  —  Correlation  of  the 
three  systems  just  described,  and  of  the  terms  used  in  con- 
nection with  each,  is  now  in  order.  In  the  first  column  is 
the  nomenclature  of  system  (A),  with  the  horizon  for  the 
reference  plane;  in  the  second  column,  the  terminology  of 
system  (£),  in  which  the  celestial  equator  is  the  funda- 


Philosophy  of  the  Celestial  Sphere 


mental  plane ;  and  in  the  third  column  are  found  the 
corresponding  points,  planes,  and  elements  referred  to 
the  ecliptic  system  (C):  — 

THE  PHILOSOPHY  OF  THE  CELESTIAL  SPHERE 


IN  THE  HORIZON  SYSTEM  (A  ) 

BECOMES  IN  THE  EQUATOR 
SYSTEM  (B) 

BECOMES  IN  THE  ECLIPTIC 
SYSTEM  (C) 

Horizon 
Vertical  circle 
Zenith 
Meridian 
Prime  vertical 

Celestial  equator 
Hour  circle 
North  pole 
Equinoctial  colure 
Solstitial  colure 

Ecliptic 
Ecliptic  meridian 
N.  pole  of  the  ecliptic 
Ecliptic  meridian 
Solstitial  colure 

Azimuth  {negative) 
Altitude 

Right  ascension 
Declination  (N.) 

Celestial  longitude 
Celestial  latitude  (N.) 

These  three  systems  of  planes  and  circles  of  the  celes- 
tial sphere  comprise  all  those  used  by  astronomers,  ex- 
cept in  the  very  advanced  investigations  of  mathematical 
and  stellar  astronomy. 


CHAPTER    IV 

THE   STARS   IN  THEIR   COURSES 

THE  fundamental  framework  for  our  knowledge  of  the 
heavens  may  now  be  regarded  as  complete.      We 
next  consider  its  relations  from  different  points  of 
view  on  earth,  at  first  filling  in  details  of  the  stars  as  neces- 
sary points  of  reference  in  the  sky. 

The  Constellations.  —  In  a  very  early  age  of  the  world, 
the  surface  of  the  celestial  sphere  was  imagined  to  be  cov- 
ered by  figures,  human  and  other,  connecting  different 
stars  and  groups  of  stars  together  in  a  fashion  sometimes 
clear,  though  usually  grotesque.  The  groups  of  stars 
making  up  these  imaginary  figures  in  different  parts  of 
the  sky  are  called  constellations.  Eudoxus  (B.C.  370)  bor- 
rowed from  Egyptian  astronomers  the  conception  of  the 
celestial  sphere,  bringing  it  to  Greece,  and  first  outlining 
upon  it  the  ecliptic  and  equator  with  the  more  prominent 
constellations.  About  60  are  well  recognized,  although  the 
whole  number  is  nearly  twice  as  great.  This  ancient,  and 
in  most  respects  inconvenient,  method  of  naming  and 
designating  the  stars  is  retained  to  the  present  day.  In 
general,  small  letters  of  the  Greek  alphabet  are  used  to 
indicate  the  more  prominent  stars  of  a  constellation,  a 
representing  its  brightest  star,  ft  the  next,  7  the  third, 
and  so  on.  The  Greek  letter  is  followed  by  the  Latin 
genitive  of  name  of  constellation ;  thus  a  Orionis  is  the 
most  conspicuous  star  in  the  constellation  of  Orion,  7  Vir-, 
ginis  is  the  third  star  in  order  of  brightness  in  Virgo,  and 

59 


60  The  Stars  in  their  Courses 

so  on.     Following  are  these  letters,  written  either  as  sym- 
bols, or  as  the  English  names  of  these  symbols :  — 


a   Alpha 

rj  Eta 

v  Nu 

T   Tau 

ft  Beta 

(9  Theta 

£Xi 

v    Upsi'lon 

y  Gamma 

i    Iota 

o  Omi'cron 

<f>  Phi 

8  Delta 

K  Kappa 

TT  Pi 

X   Chi 

c    Epsi'lon 

A  Lambda 

p  Rho 

$  Psi 

C  Zeta 

p.  Mu 

a-  Sigma 

o>  Omeg'a 

A  few  constellations  embrace  more  than  24  stars  requir- 
ing especial  designation,  and  for  these  the  letters  of  the 
Latin  alphabet  are  employed ;  and  if  these  are  exhausted, 
then  ordinary  Arabic  numerals  follow.  Thus  stars  may 
be  designated  as  F  Tauri,  31  Aquarii,  and  so  on.  About 
100  conspicuous  stars  have  other  and  proper  names,  mostly 
Arabic  in  origin  :  thus  Vega  is  but  another  name  for  a 
Lyrae,  Aldeb'aran  for  a  Tauri,  Merak  for  /5  Ursae  Majoris. 
The  lucid  stars,  or  stars  visible  to  the  naked  eye,  are 
divided  into  six  classes,  called  magnitudes.  Of  the  first 
magnitude  are  the  20  brightest  stars  of  the  firmament, 
and  the  number  increases  roughly  in  geometric  proportion. 
Of  the  sixth  magnitude  are  those  just  visible  to  the  naked 
eye  on  clear,  moonless  nights.  On  page  423  are  given 
the  names  of  the  brightest  stars ;  and  from  Plates  in  and 
iv  can  be  found  their  location  in  the  sky. 

Convenient  Maps  of  the  Stars.  —  On  the  star  maps  given  as  Plates 
in  and  iv  are  shown  all  the  brighter  stars  ever  visible  in  the  United 
States.  In  each  plate  the  lower  or  dark  chart  is  a  faithful  tran- 
script of  the  *  unlanterned  sky,'  and  the  upper  map  is  merely  a  key  to 
the  lower.  Notwithstanding  their  small  scale,  the  asterisms  are  readily 
traceable  from  the  dark  charts,  and  the  names  of  especial  stars  and 
constellations  are  then  quickly  identified  by  means  of  the  keys.  To 
connect  the  charts  with  the  sky,  conceive  the  celestial  sphere  re- 
duced to  the  size  of  a  baseball.  At  its  north  pole  place  the  center 
of  the  circular  map  (Plate  in)  ;  and  imagine  the  rectangular  map 
(Plate  iv)  as  wrapped  round  the  middle  of  the  ball,  the  central  hori- 


Constellation  Study  61 

zontal  line  of  the  chart  coinciding  with  the  equator  of  the  ball.  Just 
as  the  maps,  if  actually  applied  to  a  baseball,  would  not  make  a  perfect 
cover  for  it  without  cutting  and  fitting,  so  there  will  be  found  some 
distortion  in  comparing  the  maps  with  the  actual  sky,  especially  near 
the  top  and  bottom  of  the  oblong  chart.  Whatever  the  season  of  the 
year,  the  charts  are  easy  to  compare  with  the  sky,  by  remembering  that 
(for  8  P.M.)  Plate  in  must  be  held  due  north,  and  the  book  turned  so 
that  the  month  of  observation  appears  at  the  top  of  the  round  chart,  or 
vertically  above  Polaris,  which  is  near  the  center  of  the  map.  The 
asterisms  immediately  adjacent  to  the  name  of  the  month  will  then  be 
found  at  or  near  the  observer's  zenith.  Similarly  with  Plate  iv :  face 
due  south,  and  at  8  P.M.  stars  directly  under  the  month  will  be  found 
near  the  zenith,  and  the  oblong  chart  will  overlap  the  circumpolar  one 
about  half  an  inch,  or  30°.  At  the  middle  of  the  rectangular  chart, 
under  the  appropriate  month,  are  found  the  stars  upon  the  celestial 
equator ;  and  at  the  bottom  of  the  map.  the  constellations  faintly  visi- 
ble near  the  south  horizon.  Every  vertical  line  on  this  chart  coincides 
with  the  observer's  meridian  at  eight  ©''clock  in  the  evening  of  the 
month  named  at  the  top.  If  the  hour  of  observation  is  other  than  this, 
allow  two  hours  for  each  month ;  for  example,  at  10  P.M.  in  November 
the  stars  underneath  'DECEMBER'  will  be  found  on  the  meridian. 
Likewise  Plate  in  must  be  turned  counter-clockwise  with  the  lapse  of 
time,  at  the  rate  of  one  month  for  two  hours.  If,  for  example,  we 
desire  to  inspect  the  north  polar  heavens  at  6  P.M.  in  December,  we 
should  hold  the  book  upright,  with  November  at  the  top. 

Constellations  of  Circumpolar  Chart — Most  notable  is 
Ursa  Major,  the  Great  Bear,  near  the  bottom  (Plate  in). 
Its  seven  bright  stars  are  familiarly  known  in  America 
as  the  'Dipper,'  and  in  England  as  *  Charles's  Wain,'  or 
wagon.  Of  these,  the  pair  farthest  from  the  handle  are 
called  '  the  Pointers,'  because  a  line  drawn  through  them 
points  toward  the  pole  star,  as  the  arrow  shows.  The 
Pointers  are  five  degrees  apart,  and,  being  nearly  always 
above  the  horizon,  are  a  convenient  measure  of  large 
angular  distances.  At  the  bend  of  the  dipper  handle  is 
Mizar,  and  very  near  it  a  faint  star,  Alcor.  When  Mizar 
is  exactly  above  or  below  Polaris,  both  stars  are  on  the  true 
meridian,  and  therefore  indicate  true  north  (page  116). 
The  Pointers  readily  show  Polaris,  a  second  magnitude  star 


62  The  Stars  in  their  Courses 

(near  the  center  of  Plate  in).  No  star  of  equal  brightness 
is  nearer  to  it  than  the  Pointers.  From  Polaris  a  line  of 
small  stars  curves  toward  the  handle  of  the  Dipper,  meet- 
ing the  upper  one  of  a  pair  of  the  third  magnitude.  This 
pair,  with  another  farther  on  and  parallel  to  it,  form  the 
'  Little  Dipper,'  Polaris  being  the  end  of  its  handle.  The 
group  is  Ursa  Minor.  Opposite  the  handle  of  the  great 
Dipper,  and  at  about  the  same  distance  from  Polaris,  are 
five  rather  bright  stars  forming  a  flattened  letter  W.  They 
are  the  principal  stars  of  Cassiopeia. 

Learning  the  Constellations.  —  With  these  slender  foun- 
dations, once  well  and  surely  laid,  familiarity  with  the 
northern  constellations  is  soon  acquired.  It  is  excellent 
practice  to  draw  the  constellations  from  memory,  and  then 
compare  the  drawings  with  the  actual  sky.  An  hour's 
watching,  early  in  a  September,  evening,  will  show  that 
the  Dipper  is  descending  toward  the  northwest  horizon, 
and  Cassiopeia  rising  from  the  northeast.  Nearly  over- 
head is  Vega.  Capella,  the  large  star  near  the  right  of 
Plate  in,  will  soon  begin  to  twinkle  low  down  in  the  north- 
east. Familiarity  with  the  northern  constellations  is  the 
prime  essential,  and  they  should  be  committed,  independ- 
ently of  their  relations  to  the  horizon  at  a  particular  time ; 
for  at  some  time  of  the  year  all  these  constellations  will 
appear  inverted.  Make  acquaintance  with  them  so  thor- 
ough that  each  is  recognized  at  a  glance,  no  matter  what 
its  relation  to  the  horizon  may  be. 

Constellations  of  the  Equatorial  Girdle.  —  All  the  more 
important  ones  are  named  on  the  key  to  Plate  iv.  None 
is  more  striking  than  Orion,  whose  brilliance  is  the  glory 
of  our  winter  nights.  Hard  by  is  Sirius,  brightest  of  all 
the  stars  of  the  firmament,  which,  with  Procyon  and  the 
two  principal  stars  of  Orion,  forms  a  huge  diamond,  inter- 
sected by  the  solstitial  colure,  or  Vlth  hour  circle.  East- 


XXIV71 


xvnr 


XII 


CORONA        *r\ 

BOREALIS\  \    . 


KEY  TO  CHART  OF  EQUAT 

[The  stars  under  the  name  of  the  month 


NOVEMBER    I      OCTOBER      I   SEPTEMBER  I        AUGUST       I          JULY          I         JUNE        I 


IV.— THE  EQUAT< 


Capella  '  ',  o's E  U  8 

V          .:••::'.?>"  •  ANDROMEDA 

;  Algol* 


u,  GIRDLE  oi?  THE  STARS 

on  the  meridian  (looking  south)  at  8  P.M.] 


I    APRIL    I    MARCH    I  FEBRUARY  I   JANUARY   I  DECEMBER  I  NOVEMBER 


J,  GIRDLE  OF  THE  STARS 


Constellation  Study 


ward  from  Procyon  to  Regulus  may  be  formed  a  vast 
triangle ;  and  still  farther  east,  with  Spica  and  Arcturus, 
one  vaster  still.  By  means  of  similar  arbitrarily  chosen 
figures,  as  in  the  key,  all  the  constellations  may  readily 
be  memorized,  one  after  another,  until  the  cycle  of  the 
seasons  is  complete.  Also  the  ecliptic's  sinuous  course 
is  easy  to  trace,  from  Aries  round  to  Aries  again. 


Astral  Lantern  for  tracing  Constellations 

Helps  to  Constellation  Study.  —  Perhaps  the  easiest  to  use  and  in 
every  way  the  most  convenient  is  the  planisphere.  By  its  aid  all  the 
visible  constellations  may  be  expeditiously  traced,  the  times  of  rising 
and  setting  of  the  sun,  planets,  and  stars  found,  and  a  variety  of  simple 
problems  neatly  solved.  Another  excellent  help  in  learning  the  con- 
stellations is  the  astral  lantern  devised  by  the  late  James  Freeman 
Clarke.  The  front  side  of  the  box  is  provided  with  a  ground  glass  slide. 
In  front  of  and  into  the  grooves  of  this  may  be  slipped  cards,  figured 
with  the  different  asterisms,  as  indicated  in  the  illustration.  But  the 
peculiar  effectiveness  of  the  lantern  consists  in  the  minute  punctures 
through  the  cards,  the  size  of  each  puncture  being  graduated  according 
to  the  magnitude  of  the  star.  Bailey's  astral  lantern  is  a  similar  device 


64  The  Stars  in  their  Courses 

for  a  like  purpose.  Also  a  celestial  globe  is  sometimes  used  in  learning 
the  constellations,  but  the  process  is  attended  with  much  difficulty 
because  the  constellations  are  all  reversed  on  the  surface  of  the  globe, 
and  the  observer  must  imagine  himself  at  the  center  of  it  and  looking 
outward.  Plainly  marked  upon  the  globe  are  many  of  the  circles  of 
System  (/?),  — equator,  colures,  and  parallels  of  declination.  Also  usu- 
ally the  ecliptic.  See  illustration  on  page  71.  The  globe  turns  round  in 
bearings  at  the  poles,  fastened  to  a  heavy  meridian  ring  M  M  which  can 
be  slipped  round  in  its  own  plane  through  slots  in  the  horizon  circle  H. 
The  process  of  setting  the  globe  to  correspond  to  the  aspect  of  the 
heavens  at  any  time  is  called  rectifying  the  globe.  Bring  the  meridian 
ring  into  the  plane  of  the  meridian,  and  elevate  the  north  pole  to  an 
angle  equal  to  the  latitude.  On  pages  70,  71,  and  72  are  globes  recti- 
fied to  the  latitudes  indicated. 

Farther  Helps.  —  If  complete  knowledge  of  the  firmament  is  desired, 
a  good  star  atlas  is  the  first  essential,  such  as  have  been  prepared  with 
great  care  by  Proctor,  and  Klein,  and  Sir  Robert  Ball,  and  Upton. 
These  handy  volumes  quickly  give  a  familiarity  with  the  nightly  sky 
which  hurries  the  learner  on  to  the  possession  of  a  telescope.  By  a 
list  or  catalogue  of  celestial  objects  may  be  found  any  celestial  body, 
though  not  mapped  in  its  true  position  on  the  charts,  if  an  equatorial 
mounting  like  the  model  illustrated  on  page  53  is  constructed.  A 
mere  pointer  in  place  of  the  tube  will  make  it  into  that  convenient 
instrument  called  Rogers's  'star  finder.'  The  simplest  of  telescopes 
must  not  be  despised  for  a  beginning.  Astronomy  with  an  Opera 
Glass,  by  Serviss,  shows  admirably  what  may  be  done  with  the  slight- 
est optical  aid.  When  a  3-inch  telescope  becomes  available,  there  is  a 
multitude  of  appropriate  handbooks,  none  better  than  Proctor's  Half 
Hours  with  the  Stars.  Follow  it  with  Webb's  Celestial  Objects  for 
Common  Telescopes,  a  veritable  storehouse  of  celestial  good  things. 

The  Zodiac.  —  Imagine  parallels  of  celestial  latitude  as 
drawn  on  either  side  of  the  ecliptic,  at  a  distance  of  8° 
from  it ;  this  belt  or  zone  of  the  sky,  16°  in  width,  is  called 
the  zodiac.  Neither  the  moon  nor  any  one  of  the  bright 
planets  can  ever  travel  outside  this  belt.  About  2000 
years  ago  both  ecliptic  and  zodiac  were  divided  by  Hip- 
parchus,  an  early  Greek  astronomer,  into  twelve  equal 
parts,  each  30°  in  length,  called  the  signs  of  the  zodiac. 
The  names  of  the  constellations  which  then  corresponded 
to  them  have  already  been  given  in  their  tru^  order  on 


The  Zodiac  65 

page  40;  but  the  lapse  of  time  has  gradually  destroyed 
this  coincidence,  as  will  be  explained  at  the  end  of  Chap- 
ter vi.  In  the  figure  the  horizontal  ellipse  represents  the 
ecliptic,  and  at  the  beginning  of  each  sign  is  marked  its 
appropriate  symbol.  E  is  the  pole  of  the  ecliptic,  P 
the  north  celestial  pole,  and  the  inclined  ellipse  shows 
where  the  equator  girdles  the  celestial  sphere.  The  signs 


Celestial  Sphere  and  Signs  of  the  Zodiac 

of  the  ecliptic  girdle  have  from  time  immemorial  been 
employed  to  symbolize  the  months  and  the  round  of  sea- 
sons ;  and  a  type  of  ancient  Arabian  zodiac  is  embossed 
on  the  cover  of  this  book,  reproduced  from  Flammarion. 
The  signs  of  the  zodiac  are  discarded  in  the  accurate 
astronomy  of  to-day ;  and  the  positions  of  the  heavenly 
bodies  are  now  designated  with  reference  to  the  ecliptic, 
not  by  the  sign  in  which  they  fall,  but  by  their  celestial 
TODD'S  ASTRON.  —  5 


66 


The  Stars  in  their  Courses 


longitude.  Conventionalized  symbols  of  the  signs  of  the 
zodiac,  and  the  position  of  the  zero  point  of  each  sign, 
are  shown  on  the  sphere  on  the  preceding  page,  beginning 
with  o°  of  Aries  at  D,  and  proceeding  counter-clockwise 
as  the  sun  moves,  or  contrary  to  the  direction  the  arrow. 

How  to  locate  the  Equinoxes  among  the  Stars.  —  On 
the  earth  the  longitude  of  places  is  reckoned  from  prime 
meridians  passing  through  well-known  places  of  national 


/    OF  PEGASUS 
LPHERATZ 


VERNALTgCfQUINOX 


NORTH 
EAST 


How  to  locate  the  Vernal  Equinox 

importance.  But  the  equinoctial  colure,  the  prime  merid- 
ian of  the  heavens,  is  a  purely  imaginary  circle,  and  is  not 
marked  in  any  such  significant  manner,  as  we  should  nat- 
urally expect,  by  means  of  brilliant  stars.  It  is,  however, 
important  to  be  able  to  point  out  the  equinoxes  roughly 
among  the  stars.  The  vernal  equinox  is  above  the  hori- 
zon at  convenient  evening  hours  in  autumn  and  winter. 
Its  position  may  be  found  by  prolonging  a  line  (hour  circle) 
from  Polaris  southward  through  Beta  Cassiopeiae,  as  in 
the  above  illustration. 


How  to  Locate  the  Ecliptic  67 

This  will  be  about  30°  in  length.  Thirty  degrees  farther  in  the 
same  direction  will  be  found  the  star  Alpheratz  (Alpha  Andromedae), 
equal  in  brightness  with  Beta  Cassiopeiae.  Then  as  the  equinox  is  a 
point  in  the  equator,  and  the  equator  is  90°  from  the  pole,  we  must  go 
still  farther  south  30°  beyond  Alpheratz;  and  in  this  almost  starless 
region  the  vernal  equinox  is  at  present  found.  It  will  hardly  move 
from  this  point  appreciably  to  naked-eye  observation  during  a  hundred 
years.  This  quadrant  of  an  hour  circle  (from  Polaris  to  the  vernal 
equinox)  will  be  very  nearly  a  quadrant  of  the  equinoctial  colure  also. 
Because  Alpheratz  and  Beta  Cassiopeiae  are  very  near  it,  their  right 
ascension  is  about  o  hours.  Through  spring  and  summer  the  autumnal 
equinox  will  be  above  the  horizon  at  convenient  evening  hours.  This 
equinox,  like  the  other,  has  no  bright  star  near  it ;  roughly  it  is  about 
f  of  the  way  from  Spica  (Alpha  Virginis)  westward  toward  Regulus 
(Alpha  Leonis),  as  shown  in  the  following  diagram. 


SOUTH    HORIZON 

How  to  locate  the  Autumnal  Equinox 

How  to  locate  the  Ecliptic  (approximately)  at  Any  Time. 
-  It  will  add  much  to  the  student's  interest  in  these  purely 
imaginary  circles  of  the  sky  if  he  is  able  to  locate  them 
(even  approximately)  at  any  time  of  the  day  or  night. 
Only  two  points  in  the  sky  are  necessary.  By  day  the 
sun  is  a  help,  because  his  center  is  one  point  in  the  ecliptic. 
If  the  moon  is  above  the  horizon,  that  will  be  another 


68  The  Stars  in  their  Courses 

point,  approximately.  Then  imagine  a  plane  passed 
through  sun  and  moon  and  the  point  of  observation,  and 
that  will  indicate  where  the  ecliptic  lies.  Also,  if  the 
moon  is  within  three  or  four  days  of  the  phase  known 
as  the  'quarter,'  her  shape  will  show  very  nearly  the  direc- 
tion of  the  ecliptic  in  this  manner :  Join  the  cusps  by 
an  imaginary  line,  and  the  perpendicular  to  this  line, 
extended  both  ways,  will  mark  out  the  ecliptic  very  nearly. 
In  early  evening,  the  problem  is  easier.  On  about  half 
the  nights  of  the  year  the  moon  will  afford  one  point. 
Usually  one  or  more  of  the  brighter  planets  (Venus,  Mars, 
Jupiter,  Saturn)  will  be  visible,  and  it  has  already  been 
shown  how  to  distinguish  them  from  the  brightest  of  the 
fixed  stars.  Like  the  moon,  these  planets  never  wander 
far  from  the  ecliptic ;  and  if  we  pass  our  imaginary  plane 
through  any  two  of  them,  the  direction  of  the  ecliptic  may 
be  traced  upon  the  sky. 

If  moon  and  planets  are  invisible,  the  positions  of  known  stars  are 
all  that  we  can  rely  upon,  and  there  are  few  very  bright  stars  near  the 
ecliptic.  The  Pleiades  and  Aldebaran  (Alpha  Tauri)  are  easy  to  find 
all  through  autumn  and  winter,  and  the  ecliptic  runs  midway  between 
them.  Through  winter  and  spring,  the  l sickle'  in  Leo  is  prominent,  and 
Regulus  (Alpha  Leonis)  is  only  a  moon's  breadth  from  the  true  eclip- 
tic. Through  the  summer  Spica  (Alpha  Virginis)  is  almost  as  favor- 
ably placed ;  and  Antares  (Alpha  Scorpii)  rather  less  so,  but  not 
exceeding  10  moon  breadths  south  of  the  ecliptic.  And  in  late  sum- 
mer and  autumn,  Delta  Capricorni,  much  fainter  than  all  those  pre- 
viously mentioned,  shows  where  the  ecliptic  lies  through  a  region 
almost  wholly  devoid  of  very  bright  stars.  As  the  stars  before  named 
are  so  set  in  the  firmament  that  at  least  two  of  them  must  always  be 
above  the  horizon,  they  show  approximately  where  the  ecliptic  lies. 

Finding  the  Latitude.  —  Having  shown  how  the  stars 
and  constellations  may  be  learned  in  our  latitudes,  it  is 
next  necessary  to  find  how  their  courses  seem  to  change, 
as  seen  from  other  parts  of  the  earth.  It  is  plain  that 
going  merely  east  or  west  will  not  alter  their  courses. 


Latitude  Equals  Altitude  of  Pole  69 


The  effect  of  changing  one's  latitude  must  therefore  be 
ascertained.  Observe  Polaris  :  attention  has  already  been 
directed  to  the  fact  that  in  middle  northern  latitudes,  as 
the  United  States,  it  is  about  halfway  up  from  the  north- 
ern horizon  to  the  zenith.  The  true  north  pole  of  the 
heavens  is  i°  15',  or  two  and  a  half  moon  breadths  from 
it.  If  you  had  a  fine  in- 
strument of  the  right  kind, 
and  the  training  of  a  skill- 
ful astronomer,  you  could 
measure  accurately  the 
altitude  of  the  pole  star 
when  exactly  below  the 
pole.  Measure  it  again 
12  hours  later,  and  it  would 
be  directly  above  that  point. 
The  average  of  the  two 
altitudes,  with  a  few  slight 
but  necessary  corrections, 
would  be  the  true  altitude  of  the  center  of  the  little  circle  in 
which  the  pole  star  seems  to  move  round  once  each  day. 
This  center  is  the  true  north  celestial  pole ;  and  whatever 
its  altitude  may  be  found  to  be,  a  facile  proof  by  geome- 
try shows  that  it  must  be  equal  to  the  north  latitude  of  the 
place  where  the  observations  were  made. 

Latitude  equals  Altitude  of  Pole. — Whether  the  earth 
is  considered  a  sphere  or  an  oblate  spheroid,  the  angle 
which  the  plumb-line  at  any  place  makes  with  the  terres- 
trial equator  is  equal  to  the  latitude  (figure  above).  As 
the  plane  of  celestial  equator  is  simply  terrestrial  equator- 
plane  extended,  the  declination  of  the  zenith  is  the  same 
angle  as  the  latitude.  Now  consider  the  two  right  angles 
at  the  point  of  observation ;  (a)  the  one  between  celestial 
equator  and  pole,  and  (b)  the  other  between  horizon  and 


Latitude  equals  Altitude  of  Pole 


The  Stars  in  their  Courses 


zenith  :  the  angle  between  pole  and  zenith  is  a  common 
part  of  both.  So  the  decimation  of  the  zenith  is  equal 
to  the  altitude  of  the  pole.  Therefore  the  altitude  of  the 
pole  at  any  given  place  is  equal  to  tJie  latitude  of  that  place. 
Going  North  the  Pole  Star  rises.  —  If,  then,  one  were 
to  go  north  on  the  surface  of  the  earth  i°,  the  pole  of  the 
northern  heavens  must  seem  to  rise  i°.  For  example,  if 
the  latitude  is  42°,  one  would  have  to  travel  due  north  48° 
(3300  miles)  in  order  to  reach  the  north  pole  of  the  earth. 

And  as  the  altitude  of  the 
celestial  pole  would  have  in- 
creased 48°  also,  evidently 
this  point  and  the  zenith 
would  exactly  coincide.  To 
|H  all  adventurous  explorers  who 
may  ever  reach  the  north 
pole,  we  may  be  sure  that  the 
pole  star  will  be  all  the  time 
very  nearly  overhead,  and 
travel  round  the  zenith  once 
every  day  in  a  small  circle 
whose  diameter  would  require 
about  five  moons  to  reach 
across.  All  other  stars  would 
seem  to  travel  round  it  in 
circles  parallel  to  it  and  to  the  horizon  also.  This  peculiar 
motion  of  the  stars  as  seen  from  the  north  pole  was  the 
origin  of  the  term  parallel  sphere. 

Daily  Motion  of  the  Stars  at  the  North  Pole.  —  At  the 
north  pole  the  directions  east  and  west,  as  well  as  north, 
vanish,  and  one  can  go  only  south,  no  matter  what  way 
one  may  move.  As  seen  from  the  north  pole,  the  stars  all 
move  round  from  left  to  right  perpetually,  in  small  circles 
parallel  to  the  horizon.  Consequently  they  never  rise  or 


Parallel  Sphere  (at  the  Poles) 


Daily  Motion  of  the  Stars 


set.  All  visible  stars  describe  their  own  almucantars  once 
every  day.  Their  altitudes  are  constant,  and  their  azimuths 
are  changing  uniformly  with  the  time.  The  azimuths  of  all 
stars  change  with  equal  rapidity,  no  matter  what  their 
declination  may  be.'  These  are  the  phenomena  of  the 
parallel  sphere.  All  the  stars  north  of  the  equator  are 
always  above  the  horizon,  day  and  night.  None  of  those 
south  of  the  equator  can  ever  be  seen.  If  the  observer 
were  at  the  south  pole  of  our  globe,  the  daily  motion  of 
the  stars  relatively  to  the 
horizon  would  be  exactly  the 
same  as  at  the  north  pole; 
but  they  would  all  seem  to 
travel  round  from  right  to 
left.  The  stars  of  the  hemi-H| 
sphere  which  could  be  seen 
all  the  time  would  be  those 
which  from  the  north  pole 
could  never  be  seen  at  all. 

Daily  Motion  of  the  Stars 
in  the  United  States. —  We 
have  now  returned  from  the 
north  polar  regions  to  middle 
latitudes,  or  N.  45°,  about  that 
of  places  from  Maine  to 
Wisconsin.  The  pole  has  gone  down,  too,  and  is  elevated 
just  45°  above  the  horizon ;  consequently  the  circle  of  per- 
petual apparition,  or  parallel  of  north  declination  which  is 
tangent  above  the  north  horizon,  has  shrunk  to  a  diameter 
of  90°  on  the  sphere.  Any  star  ever  seen  between  the 
zenith  and  the  north  horizon  can  never  set.  Similarly 
the  circle  of  perpetual  occultation  must  be  90°  in  breadth : 
it  is  the  parallel  of  south  declination  which  is  tangent 
below  the  south  horizon.  Therefore  the  breadth  of  the 

/^€B^x 

K  UNIVERSTTV  1 


Oblique  Sphere  (Northern  U.  S.) 


The  Stars  in  their  Courses 


N.P 


Circ'es  of  Perpetual  Apparition  and  Perpetual 
Occultation 


middle  zone  of  stars, 
partly  above  and 
partly  below  the  hori- 
zon, is  90°.  The  quad- 
rant from  the  zenith 
to  the  south  horizon 
is  the  measure  of  its 
breadth  when  above 
the  horizon,  and  the 
distance  from  the 
north  horizon  to  the 
nadir  is  its  width  when 
below  the  horizon. 
As  at  the  arctic  circle, 
so  here  —  the  celes- 
tial equator  marks  the  middle  of  the  zone.  All  the 
stars  in  the  northern  half  of  it  are  visible  longer  than 
they  are  invisible,  and  the  farther  north  they  are,  the 
longer  they  are  above  the 
horizon.  In  the  same  way 
all  the  stars  of  this  zone 
whose  declination  is  south 
are  invisible  longer  than 
they  are  visible,  and  the 
greater  their  south  declina- 
tion, the  longer  they  are 
below  the  horizon.  It  has 
now  been  shown  how  the 
apparent  motions  of  the  stars 
are  accounted  for  by  the 
geometry  of  the  sphere. 

Daily  Motion  of  the  Stars 
at  the  Equator.  —  Here  our 
latitude  is  zero  ;  and  as  the  Right  Sphere  (at  Equator) 


Equatorial  at  Different  Latitudes  73 


altitude  of  the  north  celestial  pole  is  always  equal  to  the 
north  latitude,  the  north  pole  must  now  be  in  the  horizon 
itself.  As  the  poles  are  180°  apart,  evidently  the  south 
pole  of  the  heavens  must  now  be  in  the  south  horizon. 
The  equator,  then,  must  pass  through  the  zenith,  and  the 
stars  can  rise,  pass  over, 
and  set,  in  vertical  planes 
only,  whence  the  name 
rig  Jit  sphere,  A  star's 
diurnal  circle,  therefore, 
is  coincident  with  its 
parallel  of  declination. 
But  what  is  now  the 
size  of  the  circles  of  per- 
petual apparition  and 
occupation  ?  It  is  evi- 
dent that  they  must 
have  shrunk  in  dimen- 
sions more  and  more  as 
we  journeyed  south. 
The  circle  of  perpetual 
apparition  is  now  a  mere 
point,  —  the  north  pole 
itself ;  and  the  circle  of 

perpetual  occupation  is  a  point  also,  —  the  south  pole. 
No  star,  then,  can  be  visible  all  the  time,  nor  can  any 
be  invisible  all  the  time.  The  equatorial  zone  of  stars, 
visible  part  of  the  time  and  invisible  the  remainder  of 
each  day  of  24  hours,  has  expanded  to  embrace  the  entire 
firmament.  Every  star,  no  matter  what  its  declination,  is 
above  the  horizon  12  sidereal  hours  and  below  it  12  hours, 
and  so  on  alternately  forever. 

The  Equatorial   at  Different  Latitudes.  —  Remembering 
that  the  principal  axis  of   the  equatorial  telescope  must 


Equatorial  at  the  Poles 


74 


The  Stars  in  their  Courses 


always  be  directed  toward  the  pole  of  the  heavens,  it  is 
easy  to  see  what  the  construction  of  the  instrument  must 
be,  to  adapt  it  for  use  in  different  latitudes.  At  the  pole 
itself,  were  an  equatorial  telescope  required  for  that  lati- 
tude, the  polar  axis 
would  be  vertical  (pre- 
ceding page);  and  the 
equatorial  would  not 
differ  at  all  from  the 
altazimuth.  As  we 
travel  from  the  pole 

^J*^P|S  into    lower   latitudes, 

\1  ^""^"H  fill  tne  P°lar  axis  is  tilted 

from  the  vertical  ac- 
cordingly ;  until  at  the 
equator  it  becomes  ac- 
tually horizontal,  as 
illustrated  adjacent. 
An  equatorial  mount- 
ed at  middle  latitudes 
has  already  been 
shown  on  page  53. 

It  must  not  be  thought  that  this  change  of  latitude  and  cor- 
responding inclination  of  the  polar  axis  modifies  in  any 
way  the  relations  of  other  parts  of  the  equatorial.  The 
polar  axis  is  always  in  the  meridian;  and  its  altitude, 
or  the  elevation  of  its  poleward  end,  is  always  equal  to 
the  latitude.  The  polar  axes  of  equatorial  telescopes 
in  all  the  observatories  of  the  world  are  parallel  to  one 
another. 


Equatorial  at  the  Equator 


Large  equatorial  mountings,  or  those  rigid  enough  to  carry  a  tele- 
scope above  six  inches  aperture,  always  have  the  frame  or  pier  head 
cast  by  the  maker  in  such  form  that  the  bearing  for  the  polar  axis  shall 
stand  at  the  angle  required  by  the  latitude  of  the  place  where  the  tele- 


Equatorial  at  Different  Latitudes  75 

scope  is  to  be  used ;  smaller  instruments,  called  portable  equatorials, 
generally  have  the  bearing  of  the  polar  axis  attached  to  the  pier,  stand, 
or  tripod,  by  means  of  a  rigid  clamp ;  the  polar  axis  can  then  be  tilted 
to  correspond  to  any  required  latitude,  as  shown  by  a  graduated  quadrant 
or  otherwise.  Such  portable,  or  universal,  equatorials  are  an  essential 
part  of  the  equipment  of  eclipse  and  other  astronomical  expeditions. 
As  the  polar  axis  is  reversed,  end  for  end,  in  passing  from  one  hemi- 
sphere to  the  other,  the  clockwork  motion  must  be  reversible  also, 
because  the  stars  move  from  east  to  west  in  both  hemispheres. 

Our  next  inquiries  are  directed  toward  the  astronomical 
relations  of  the  earth  on  which  we  dwell,  its  form  and  size, 
and  the  elementary  principles  by  which  these  facts  are 
ascertained. 


CHAPTER   V 

THE   EARTH   AS   A  GLOBE 

THE  original  idea  of  the  earth,  as  given  in  the  Homeric 
poems,  was  that  of  an  immense,  flat,  circular  plane, 
around  which   Oceanus,  a  mythical  river,   not  the 
Atlantic,  flowed  like  a  vast  stream.      It  was  thought  to 
be  bounded  above  by  a  hollow  hemisphere  turned  down- 
ward  over   it,    through   and    across    which    the    heavenly 
bodies  coursed  for  human  convenience  and  pleasure. 

Ancient  Idea  of  the  Earth.  — Anaximander  (B.C.  580)  re- 
garded the  earth  as  a  flat,  circular  section  of  a  vertical 
cylinder,  with  Greece  and  the  Mediterranean  surrounding 
the  upper  end.  Herodotus  (B.C.  460),  whose  geographic 

knowledge  was  exten- 

^ir~*        —^     g—    :^^~gjj^tf    srve>  ridiculed  the  idea 
/(\  ^W    °f  a  flat  and  circular 

Curvature  of  the  Ocean  exaggerated  earth'       T°    Plat°    (B'C' 

390),  the   earth  was  a 

cube.  Even  as  late  as  A.D.  550,  Cosmas  drew  the  earth  as 
a  rectangle,  twice  as  long  (east  and  west)  as  it  was  broad 
(north  and  south),  from  which  conception  have  originated 
the  terms  longitude  (length)  and  latitude  (breadth);  and 
from  the  four  corners  of  this  rectangular  earth  rose  pillars 
to  support  the  vault  of  the  sky.  The  venerable  Bede  (A.D. 
700)  promulgated  the  theory  of  an  egg-shaped  earth,  float- 
ing in  water  everywhere  surrounded  by  fire.  Long  before 
this,  however,  Thales  (B.C.  600)  and  Pythagoras  (B.C.  530) 
had  taught  that  the  earth  was  spherical  in  form  ;  but  the 

76 


The  Curvature  of  the  Earth  77 

erroneous  beliefs  persisted  through  century  after  century 

before    the   doctrine 

of  a  globular   earth 

was  fully  established. 

Final      doubt      was 

swept   away  by   the 

famous     voyage     of 

Magellan,      one      of 

whose      ships      first 

circumnavigated  the 

globe     in    the     i6th 

century,  and  in  three 

years  returned  to  its 

starting  point. 

How  to  see  the  Cur- 

..    , ,_      T,       , «  Ship's  Rigging  Distinct,  Water  Hazy 

vature  of  the  Earth. 

—  By  ascending  to  greater  and  greater  heights  above  the 
earth's  surface,  the  horizon  retreats  farther  and  farther. 

If  we  ascend  a  peak 
in  mid-ocean,  the  ex- 
tension of  the  radius 
of  vision  may  be  seen 
to  be  the  same  in 
every  direction,  thus 
indicating  a  spherical 
earth.  But  a  better 
experimental  proof 
may  be  had.  Near 
the  shore  of  a  large 
body  of  water,  on  a 
fine  day  when  ships 
can  be  seen  far  out, 

Water  Distinct,  Rigging  Ill-defined  ,  / 

mount  a  telescope  (as 
indicated  opposite)  upon  a  high  building  or  cliff.      The 


78  The  Earth  as  a  Globe 

intervening  water  will  be  imperfectly  seen  (page  77),  but 
the  ship's  masts  and  rigging  well  denned,  if  all  conditions 
are  favorable.  Now  draw  out  the  eyepiece  of  the  tele- 
scope until  the  waves  on  the  horizon  line  appear  sharply 
defined.  The  details  of  the  ship  will  then  be  hazy  and 
indistinct,  because  the  ship  is  farther  away  than  the  water 
which  hides  her  hull.  Repeat  the  observation  by  focusing 
the  telescope  alternately  on  the  ship  and  the  water  in  the 
same  field  of  view,  —  affording  ocular  proof  that  the 
earth's  surface  curves  away  from  the  line  of  vision. 
Wherever  this  simple  experiment  is  tried,  the  result  will 
be  the  same ;  so  we  reach  the  conclusion  that  the  earth  is 
round  like  a  ball. 


DE^VER  CHICAGO 


Earth  a  Plane,  Local  Time  everywhere  the  Same 

Telegraphic  Proof  that  the  Earth  is  Round.  —  Farther 
proof  that  the  earth  is  not  a  plane  may  be  derived  with 
the  assistance  of  the  electric  telegraph.  If  the  earth  were 
a  plane,  local  time  would  everywhere  be  the  same.  This 
condition  is  shown  in  the  above  figure,  for  Denver,  Chi- 
cago, and  New  York:  the  lines  of  direction  in  which  the 
sun  appears  from  all  three  places  are  parallel,  because 
the  distance  separating  them  is  not  an  appreciable  part 
of  the  sun's  true  distance.  Therefore,  as  the  sun's  angle 
east  of  .the  meridian  corresponds  to  10  A.M.  at  one  place, 


Measurement  of  the  Earth 


79 


it  should  be  10  A.M.  at  all.  But  at  10  A.M.  at  Chicago,  if 
the  operator  asks  New  York  and  Denver  what  time  it  is 
at  those  places,  he  will  receive  the  answer  that  it  is  9 
o'clock  at  Denver  and  1 1  at  New  York.  The  sun,  there- 
fore, must  be  15°  east  of  the  meridian  at  New  York,  as 
shown  in  the  figure  below,  30°  at  Chicago,  and  45°  at  Den- 
ver. So  the  meridian  planes  of  these  three  places  cannot 
be  parallel,  as  in  the  first  illustration,  but  must  converge 
below  the  earth's  surface,  as  shown  in  the  second  one. 

By  means  of  land  lines  and  cables,  the  local  time  has  been  compared 
nearly  all  the  way  round  the  globe,  eastward  from  San  Francisco  to 
New  York,  across  the  Atlantic  Ocean,  over  the  eastern  hemisphere, 
through  Europe  and  Asia  to  Japan.  Everywhere  it  is  found  that 


CHICAGO 


Earth  a  Globe,  Local  Time  depends  on  the  Longitude 

meridians  converge  downward  in  such  a  way  that  all  would  meet  in 
a  single  line.  This  geometric  condition  can  be  fulfilled  only  by  a 
solid  body,  all  of  whose  sections  perpendicular  to  this  common  line 
are  circles.  Therefore  the  earth  is  round,  east  and  west;  and,  by 
going  north  and  south  in  different  parts  of  the  earth,  and  continually 
observing  the  change  in  meridian  altitudes  of  given  stars,  it  is  found 
that  the  earth  is  round  in  a  north  and  south  direction  also.  But  all 
these  curvatures  as  observed  in  different  places  nearly  agree  with  each 
other ;  therefore,  the  earth  is  nearly  a  sphere. 

History  of  the  Measurement  of  the  Earth.  —  While  the 
Chaldeans  are  credited  with    having  made  the    first  esti- 


8o  The  Earth  as  a  Globe 

mate  of  the  earth's  circumference  (24,000  miles),  the 
Greeks,  beginning  with  Aristotle  (B.C.  350),  made  note- 
worthy efforts  to  solve  this  important  problem,  which  is 
preliminary  to  the  measurement  of  all  astronomical  dis- 
tances. Eratosthenes  (B.C.  240)  and  Cleomedes  (A.D.  150) 
applied  the  gnomon  to  the  measurement  of  degrees  on 
the  earth's  surface,  and  devised  the  application  of  geom- 
etry to  this  problem  essentially  as  it  is  employed  to-day. 
They  made  Syene  7°  12'  south  of  Alexandria;  and  as  the 
measurement  of  distance  between  these  places  made  them 
5000  stadia  apart,  the  proportion 

7°.  2: 360°  1:5000:— 

gave  for  the  circumference  of  the  earth  250,000  stadia,  or 
24,000  miles. 

Posidonius  (B.C.  260)  made  a  similar  determination  between  Rhodes 
and  Alexandria.  Early  in  the  ninth  century  of  our  era,  the  Arabian 
caliph  Al-Mamun  directed  his  astronomers  to  make  the  first  actual 
measurement  of  an  arc  of  a  terrestrial  meridian,  on  the  plain  of  Singar, 
near  the  Arabian  Sea.  Wooden  poles  were  used  for  measuring  rods, 
but  the  result  is  uncertain,  because  the  details  of  the  corresponding 
astronomical  observations  are  not  known.  Fernel,  in  France,  measured 
a  terrestrial  arc  early  in  the  i6th  century,  adopting  a  method  like  that 
of  Eratosthenes,  and  beginning  that  brilliant  series  of  geodetic  meas- 
ures which,  through  succeeding  centuries,  did  much  to  establish  the 
scientific  prestige  of  France.  Also  Picard  measured  an  accurate  arc  of 
meridian  in  1671,  used  by  Newton  in  establishing  his  law  of  gravitation. 

Geodesy.  —  Geodesy  is  the  science  of  the  precise  meas- 
urement of  the  earth.  Accurate  geodetic  surveys  have 
been  conducted  during  the  present  century  in  England, 
Russia,  Norway,  Sweden,  Germany,  India,  and  Peru ;  and 
eventually  the  transcontinental  measurements,  completed 
in  the  year  1897  by  the  United  States  Coast  and  Geodetic 
Survey,  will  make  a  farther  and  highly  important  contri- 
bution to  our  knowledge  of  the  size  and  figure  of  the  earth. 
Evidently  an  arc  of  a  latitude  parallel  may  make  additions 


Earth "s  Size  and   Volume  81 

to  this  knowledge,  as  well  as  an  arc  of  meridian.  In  the 
former  case  the  astronomical  problem  is  to  find  the  differ- 
ence of  longitude  between  the  extremities  of  the  measured 
arc ;  in  the  latter,  the  corresponding  difference  of  latitude. 
The  processes  of  geodesy  proper  —  that  is,  the  finding  out 
how  many  miles,  feet,  and  inches  one  station  is  from 
another  —  are  conducted  by  a  system  of  indirect  measure- 
ments called  triangulation. 

Triangulation.  —  Although  Ptolemy  (A.D.  140)  had  shown  that  an 
arc  of  meridian  might  be  measured  without  going  over  every  part  of  it, 
rod  by  rod,  the  first  application  of  his  important  suggestion  was  made 
by  Willebrord  Snell,  a  Netherland  geometer  of  the  I7th  century. 
Trigonometry  is  the  science  of  determining  the  unknown  parts  of 
triangles  from  the  known.  When  one  side  is  known  and  the  two 
angles  at  its  ends,  the  other  sid.js  can  always  be  found,  no  matter  what 
the  relative  proportions  of  these  sides.  It  is  evident,  then,  that  if  a 
short  side  lias  been  measured,  the  long  ones  may  be  found  by  the  much 
simpler,  less  tedious,  and  more  accurate  process  of  mathem'atical  calcu- 
lation. Triangulation  is  the  process  of  finding  the  exact  distance 
between  two  remote  points  by  connecting  them  by  a  series  or  network 
of  triangles.  The  short  side  of  the  primary  triangle,  which  is  actually 
measured,  foot  by  foot,  is  called  the  base.  For  the  sake  of  accuracy 
the  base  is  often  measured  many  times  over.  Thenceforward,  only 
angles  have  to  be  measured  —  mostly  horizontal  angles  ;  and  this  part  of 
the  work  is  done  with  an  altazimuth  instrument.  We  must  pass  over 
the  explanation  of  the  somewhat  complex  process  of  getting  the  single 
desired  result  from  a  rather  large  mass  of  observations  and  calcula- 
tions. The  base  must  not  be  too  short ;  and  the  stations  must  be  so 
selected  as  to  give  well-conditioned  triangles.  Of  course  an  equilateral 
triangle  is  well-conditioned  in  the  extreme,  and  good  judgment  is  re- 
quired in  deciding  how  great  a  departure  from  this  ideal  figure  is  allow- 
able. The  triangle  on  page  235,  with  the  earth's  diameter  as  a  base, 
is  exceedingly  ill-conditioned.  Snell's  base  was  measured  near  Leyden  ; 
but  it  was  shorter  than  it  should  have  been  ;  the  telescope  was  not  then 
available  for  accurate  measurement  of  angles  ;  and  some  of  his  triangles 
were  ill-conditioned,  consequently  his  result  for  the  size  of  the  earth 
was  erroneous.  The  geometers  of  to-day  employ  the  principles  of  his 
method  unchanged,  but  with  great  improvement  in  every  detail. 

Earth's  Size  and  Volume.  — As  a  result  of  such  labors,  it 
is  found  that  the  length  of  the  shortest  diameter  of  the 
TODD'S  ASTRON.  —  6 


82 


The  Earth  as  a  Globe 


CASING  OR  STOP  ON  WEST  SIDE 
OF  SOUTH  WINDOW 


earth,  or  the  distance  between  the  two  poles,  is  7900  miles. 
In  the  plane  of  the  equator,  the  diameter  of  our  globe  is 
7927  miles,  or  about  g-J^  part  greater  than  the  diameter 

through  the  poles. 
This  fraction  is  a 
little  less  than  the 
oblateness  of  the 
earth  or  its  polar 
compression.  Re- 
cent measurements 
indicate  that  the 
equator  itself  is 
slightly  elliptical, 
but  this  result  is  not 
yet  absolutely  estab- 
lished. The  form  of 
the  earth  may  there- 
fore be  regarded  as 
an  ellipsoid  with 
three  unequal  diam- 
eters, or  axes.  Know- 
ing the  lengths  of 
these  diameters,  the 
volume  of  the  earth 
has  been  calculated 

and  found  to  be  260  billion  cubic  miles.  As  the  size  of 
the  earth  was  first  determined  by  measuring  the  length 
of  a  meridian  arc,  and  comparing  it  with  the  difference  of 
latitude  at  the  two  ends  of  the  arc,  we  next  describe  an 
easy  method  of  finding  the  latitude. 

How  to  observe  the  Latitude.  —  It  is  probable  that  you 
can  take  the  latitude  of  the  place  where  you  live,  more 
accurately  from  the  map  in  any  geography,  than  you  can 
find  it  by  the  method  about  to  be  described.  But  the 


SOUTH 


The  Latitude-box  in  Position 


NORTH 


How  to  Observe  the  Latitude  83 

principle  involved  is  often  used  by  the  astronomer  and 
navigator,  and  it  is  important  to  understand  it  fully,  and 
to  test  it  practically,  although  there  may  be  at  hand  no 
instrument  better  than  a  plumb-line  and  a  pasteboard 
box. 

A  box  about  six  or  seven  inches  square  should  be  selected.     The 
depth  of  the  box  is  not  important  —  four  or  five  inches  will  be  con- 


GRADUATED  QUADRANT 

(To  be  copied  in  the  latitude-box,  for  measuring  the 
Sun's  zenith  distance  at  apparent  noon  ) 


venient.  Cut  a  hole  \  inch  square  (A}  through  the  middle  of  one 
side,  at  the  bottom.  On  the  inside  paste  a  piece  of  letter  paper  over 
this  hole,  as  indicated  by  the  dotted  line  CB  (opposite  page).  Trans- 
fer a  duplicate  of  the  above  graduated  arc  to  a  stiff  sheet  of  highly 
calendered  paper  or  very  smooth  bristol  board  about  four  inches 
square.  Trim  the  little  quadrant  accurately,  taking  especial  care  that 
the  edges  of  it  at  the  right  angle  shall  exactly  correspond  with  the 
lines.  The  quadrant  is  now  to  be  pasted  on  the  inside  of  the  bottom 
of  the  box,  in  such  a  way  that  the  center  of  the  arc,  or  the  right-angled 
point,  will  be  in  contact  with  the  bit  of  paper  pasted  over  the  aperture. 


84 


The  Earth  as  a  Globe 


One  thing  more,  and  the  latitude-box  is  complete :  exactly  opposite  the 
right-angled  apex  of  the  quadrant,  and  perhaps  a  sixteenth  of  an  inch 
away  from  its  plane,  pierce  a  pin  hole  through  the  letter  paper.  Now 
select  a  window  facing  due  south,  and  tack  the  box  on  the  west  face 
of  its  casing,  so  that  the  quadrant  will  be  nearly  in  the  meridian. 
The  illustration  on  page  82  shows  how  it  should  be  fastened.  Put  in 
a  tack  at  F.  Then  hang  a  plumb-line  by  a  fine  thread  in  front  of  the 
box,  and  sight  along  it,  turning  the  box  round  the  tack  until  the  line 

ED  is  parallel  to  the 
plumb-line.  Then  tack 
in  final  position  at  G,  and 
verify  the  direction  of  ED 
by  the  plumb-line  after- 
wards. The  latitude-box 
is  now  ready  for  use. 

To  make  the  Observa- 
tion. —  On  any  cloudless 
day,  about  half  an  hour 
before  noon,  the  sunlight 
falling  through  the  pin 
hole  will  make  a  bright 
elongated  image  at  //. 
As  the  sun  approaches 
nearer  and  nearer  the 
meridian,  this  image  will 
travel  slowly  toward  K, 
becoming  all  the  time  less 
bright,  but  more  elongate.  Just  before  apparent  noon  it  will  appear  as 
a  light  streak,  A"/.,  about  one  degree  broad,  and  stretching  across  the 
graduation  of  the  quadrant.  The  observation  is  completed  by  taking 
the  reading  of  the  middle  of  this  light  streak  on  the  arc,  to  degrees 
and  fractional  parts  as  nearly  as  can  be  estimated.  It  is  better  to  set 
down  this  reading  in  degrees  and  tenths  decimally. 

To  calculate  or  reduce  the  Observation.  —  Only  a  single  prin- 
ciple is  necessary  here,  because  in  our  latitudes  refraction  by  the  air 
(page  91)  will  never  be  an  appreciable  quantity.  Take  the  sun's  dec- 
lination from  table  on  following  page.  The  above  diagram  shows 
how  it  should  be  applied  to  the  reading  on  the  arc.  If  declination 
is  south,  subtract  it  from  the  reading  on  arc  of  the  quadrant,  and 
remainder  is  the  latitude.  But  if  sun's  declination  is  north,  add  it  to 
the  quadrant  reading,  and  the  sum  will  be  equal  to  the  latitude.  The 
quadrant  reading  is  sun's  zenith  distance ;  and  the  single  principle 
employed  is  the  fundamental  one :  that  the  altitude  of  the  pole  (or 
declination  of  zenith)  is  equal  to  the  latitude. 


Latitude  equals  Zenith  Distance  plus  Declination 


Finding  Accurate  Latitude 


The  Sun's  Declination.  —  The  sun's  declination  is  its 
angular  distance  either  north  or  south  of  the  celestial 
equator.  It  varies  from  day  to  day,  and  may  be  taken 
from  the  following  table,  with  sufficient  accuracy  for  the 
foregoing  purpose  during  the  years  1897-1900. 

THE  SUN'S  DECLINATION  AT  APPARENT  NOON 


DAY 

DECL. 

DAY 

DECL. 

DAY 

DECL. 

Jan.   i 

23°.0  S. 

May  i 

i5°.2  N. 

Aug.  29 

9°.2  N. 

ii 

21  .7  S. 

ii 

1  8  .0  N. 

Sept.  8 

5  -5N. 

21 

19  .8  S. 

21 

20  .3  N. 

18 

i  .6  N. 

31 

17  .2  S. 

31 

22  .0  N. 

28 

2  .2  S. 

Feb.  10 

14  .2  S. 

June  10 

23  .0  N. 

Oct.  8 

6  .1  S. 

20 

10  .7  S. 

20 

23  .5  N. 

18 

9  .8  S. 

Mar.  2 

7.08. 

30 

23  .2  N. 

28 

13  .3  S. 

12 

3.  IS. 

July  10 

22  .2  N. 

Nov.  7 

16  .5  S. 

22 

o  .8  N. 

20 

20  .6  N. 

17 

19  .1  S. 

Apr.  i 

4-7N. 

30 

18  .4  N. 

27 

21  .2  S. 

ii 

8  .s  N. 

Aug.  9 

15  .7N. 

Dec.  7 

22  .7  S. 

21 

12  .0  N. 

J9 

12  .6N. 

17 

23  .4  S. 

May  i 

15  .2  N. 

29 

9  .2  N. 

27 

23  .3  S. 

The  values  are  adjusted  to  every  tenth  day  through  the 
year.  Find  the  value  for  any  intermediate  date  pro- 
portionally. 

How  the  Latitude  is  found  accurately.  —  But  while  a 
crude  method  like  the  foregoing  has  a  certain  value  as 
illustrating  the  outline  of  a  principle,  it  is  of  no  impor- 
tance "to  the  astronomer,  because  of  the  impossibility  of 
eliminating  the  very  large  errors  to  which  it  is  subject. 
He  therefore  employs  a  variety  of  other  methods.  The 
best  is  the  method  of  equal  zenith  distances. 

The  instrument  for  measuring  them  is  called  the  zenith  telescope. 
Two  stars  are  selected  whose  declinations  are  such  that  one  of  them 


86 


The  Earth  as  a   Globe 


culminates  as  far  north  of  zenith  as  the  other  does  south  of  it.  The 
telescope  is  constructed  with  a  delicate  level  attached  to  its  tube,  so  that 
it  can  be  clamped  rigidly  at  any  angle.  When  the  first  star  is  observed 
set  the  level  horizontal:  then  turn  the  instrument  round  180°,  taking 

care  not  to  disturb  the  level.  The  second 
star  will  cross  the  field  of  view,  because 
the  telescope  will  now  be  pointing  as  far 
on  one  side  of  zenith  as  it  was  on  oppo- 
site side  in  the  first  position.  Declina- 
tions of  both  stars  must  be  accurately 
known ;  and  these,  with  small  corrections 
depending  upon  instrument  and  atmos- 
phere, give  the  means  of  calculating  lati- 
tude with  great  precision.  The  zenith  tel- 
escope is  usually  a  small  instrument,  per- 
haps 3  feet  high.  The  one  here  shown  is 
employed  by  Doolittle  at  the  Flower 
Observatory  of  the  University  of  Pennsyl- 
vania, in  making  the  critical  observations 
described  at  the  end  of  this  chapter.  At 
fixed  observatories  the  latitude  is  generally 

Zenith  Telescope  determined    by   means   of   the    meridian 

(Warner  &  Swasey)  circle  (described  on  page  216). 

Length  of   Degrees   of   Latitude   and   Longitude. — The 

length  of  a  degree  on  the  equator  is  69^  statute  miles. 
At  the  equator  a  degree  of  longitude  and  a  degree  of 
latitude  are  very  nearly  equal  in  length,  the  latter  being 
only  about  yj  Q-  part  longer.  Leaving  the  equator,  degrees 
of  longitude  grow  rapidly  shorter,  because  meridians 
converge  toward  the  pole.  In  latitude  30°  the  degree  of 
longitude  has  shrunk  to  60  miles,  so  that  a  minute  of  longi- 
tude is  covered  for  every  mile  traveled  east  or  west.  In 
the  United  States,  average  length  of  a  minute  of  longitude 
is  of  a  mile. 


By  measuring  degrees  of  meridian  at  various  latitudes,  they  are  found 
invariably  longer,  the  nearer  the  pole  is  approached.  So  curvature  of 
meridians  must  decrease  toward  the  pole,  because  the  less  the  curvature 
of  a  circle,  the  longer  are  degrees  upon  it.  The  figure  opposite  shows 


Terrestrial  Gravity 


this  effect  much  exaggerated,  but  actual  differences  are  not  large ;  at 
equator  the  length  of  a  degree  of  latitude  is  68%  in  the  United  States 
almost  exactly  69,  and  at  the  pole  69!  miles. 
The  angle  between  equator-plane  and  a  line       N0.  POLE 
from  any  place  to  earth's  center  is  called  its 
geocentric  latitude ;    and   the   difference    be- 
tween it  and  ordinary  or  geographic  latitude 
is  the  angle  of  the  vertical.     It  is  zero  at  poles 
and  equator,  and  amounts  to  about  11'  at  lati- 
tude 45°,  geocentric  being  always  less  than 
geographic  latitude. 


Degrees  grow  Longer 
toward  the  Poles 


Terrestrial  Gravity.  —  By  gravity 
is  meant  the  natural  force  exerted  on 
all  terrestrial  matter,  drawing  or  tend- 
ing to  draw  it  downward  in  the  direc- 
tion of  the  plumb-line.  All  objects,  as  air,  water,  buildings, 
animals,  earth,  rock,  metals,  are  held  in  position  by  this 
attraction,  and  it  gives  them  the  property  called  weight. 
As  we  know,  if  the  earth  were  dug  away  from  under  us,  we 
should  fall  to  a  point  of  rest  nearer  the  earth's  center.  If 
gravity  did  not  exist,  all  natural  objects  not  anchored  firmly 
to  earth  would  be  free  to  travel  in  space  by  themselves. 
The  ultimate  cause  of  this  force  has  not  yet  been  ascer- 
tained, but  its  law  of  action  has  been  fully  investigated 
(page  384).  It  diminishes  as  we  go  upward,  being  a  thou- 
sandth part  less  on  a  mountain  10,000  feet  high.  Gravity 
remains  constant  at  a  given  place,  and  is  exerted  upon  all 
objects  alike.  If  unobstructed,  all  fall  to  the  earth  from  a 
given  height  in  exactly  the  same  time. 

Try  the  experiment  for  yourself,  using  two  objects  to  which  the  air 
offers  very  different  resistance  —  a  silver  dollar,  and  a  piece  of  tissue 
paper  about  half  an  inch  square.  Hold  the  coin  delicately  suspended 
horizontally  between  thumb  and  finger.  Practice  releasing  the  coin  so 
that  it  will  remain  horizontal  while  dropping.  Then  place  the  paper 
lightly  on  top  of  the  coin.  The  paper  will  fall  in  exactly  the  same  time 
as  the  coin  does,  because  the  coin  has  partially  pushed  the  air  aside, 
and  permitted  gravity  to  act  upon  the  paper,  quite  unhampered  by 


88  The  Earth  as  a  Globe 

resistance  of  the  atmosphere.  The  coin  pushes  the  air  aside  and  falls 
as  quickly  as  the  paper  falls  without  pushing  the  air  aside.  But  the  fall 
of  the  coin  is  not  appreciably  delayed  by  aerial  resistance,  and  both 
coin  and  paper  fall  through  the  same  distance  in  the  same  time. 

The  Earth's  Form  found  by  Pendulums.  —  If  a  delicately 
mounted  pendulum  of  invariable  length  is  carried  from 
one  part  of  the  globe  to  another,  it  is  found  from  compari- 
son with  timepieces  regulated  by  observations  of  the  stars, 
that  its  period  of  oscillation,  or  swinging  from  one  side 
of  its  arc  to  the  other,  is  subject  to  change.  Richer  first 
tested  this  in  1672.  By  carrying  from  Paris  to  Cayenne 
a  clock  correctly  regulated  for  the  former  station,  he  found 
that  it  lost  2m.  285.  a  day  at  the  latter ;  and  it  was  necessary 
to  shorten  the  pendulum  accordingly.  Now,  conversely, 
preserve  the  length  of  the  pendulum  absolute,  and  record 
the  exact  amount  of  its  gain  or  loss  at  places  differing 
widely  in  latitude  and  longitude;  then  it  will  be  possible 
to  find  their  relative  distance  from  the  center  of  the  earth, 
because  the  law  connecting  the  oscillation  of  the  pendulum 
with  the  force  of  gravity  at  different  distances  from  the 
earth's  center  is  known.  At  the  sea  level  in  the  latitude 
of  New  York,  a  pendulum  oscillating  once  a  second  is  39.1 
inches  long,  and  the  times  of  vibration  of  pendulums  vary 
as  the  square  root  of  their  lengths.  This  kind  of  a  survey 
of  the  earth  is  called  a  gravimetric  survey,  and  opera- 
tions in  the  process  are  termed  swinging  pendulums. 

In  this  manner  it  has  been  ascertained  that  the  force  of  gravity  at 
the  earth's  poles  must  be  about  T^  greater  than  at  the  equator.  But 
in  order  to  find  the  earth's  figure,  this  result  must  be  corrected  because 
the  effect  of  the  earth's  attraction  is  everywhere  (except  at  the  poles) 
lessened  on  account  of  the  centrifugal  force  of  its  rotation.  It  is  great- 
est at  the  equator,  amounting  to  ^-  Subtracting  this  from  T^,  the 
remainder  is  about  ^i-  .  This  result  makes  the  earth's  equatorial 
radius  about  13  \  miles  longer  than  its  polar  radius,  thereby  verifying  the 
value  derived  from  the  measures  of  meridian  arcs.  Pendulum  observa- 


Weighing  tke  Earth 


tions  can  be  made  at  numerous  localities  where  the  contour  of  the 
surface  is  so  irregular  that  measurement  of  arcs  is  impracticable.  Be- 
sides this,  the  swinging  of  pendulums  has  revealed  many  interesting 
facts  regarding  the  earth's  crust ;  important  among  them  being  this  — 
that  the  mountains  of  our  globe  are  relatively  light,  and  some  of  them 
mere  shells.  American  geometers  who  have  contributed  most  to  these 
researches  are  Peirce  and  Preston. 

Weighing  the  Earth.  —  The  mass  of   the   earth  is  six 
thousand    millions   of   millions   of  millions  of   tons.     Per- 
haps this  statement  does  not  assist 
very  much   in  realizing  how  heavy          \ 
the   earth    actually  is ;    but  it  may 
arouse  interest  in  regard  to  methods 
of  reaching  such  a  result.     Several 
have  been  employed,  but  the  bare 
outline  of  the  first  one  ever  tried  is 
indicated  by  the  figure  of  a  section 
of  the  earth  surmounted  by  a  rather 
abrupt  mountain.    The  straight  lines 
drawn    downward    (one    from    the 
north  and  the  other  from  the  south 
side     of     the    mountain)   converge 
toward    the   center    of    the    earth. 
Outward  toward  the  stars  each  line 
would  point  in  the  direction  of  the 
zenith  of  the  station  a  or  b,  if  the 
mountain  were  not  there.     But  the 
attraction    of    the    mountain    mass 
draws  toward  itself  the  plumb-lines 
suspended  on  both  sides  of  it ;    so 
that  the  difference  of  latitude  of  the  two  stations  is  made 
greater  by  the  amount  that  the  angle  of  the  dotted  lines 
exceeds  the  angle  at  the  center  of  the  earth.     But  the 
true  difference  of  latitude  between  a  and  b  can  be  found 
by  surveying  round  the  mountain.     This  survey,  too,  must 


Weighing  the  Earth 


The  Earth  as  a  Globe 


be  so  extended  that  the  volume  of  the  mountain  may  be 
ascertained ;  geologists  examine  its  rock  structure,  and  its 
actual  weight  in  tons  is  calculated.  Then  by  a  mathe- 
matical process  the  earth  is  weighed  against  the  mountain, 
and  the  result  in  tons  given  above  is  obtained  from  the 
ratio  of  the  mass  of  our  globe  to  the  mass  of  the  moun- 
tain. Schiehallion  in  Scotland  was  the  mountain  first  util- 
ized in  this  important  research,  about  a  century  ago.  As 
a  result  of  all  the  measures  of  different  methods,  the 
earth's  mean  density  is  found  to  be  5.6.  This  means  that 
if  there  were  a  globe  entirely  composed  of  water  and  of 
exactly  the  same  volume  as  our  globe,  the  real  earth  would 
weigh  5.6  times  as  much  as  the  sphere  of  water. 

Atmospheric  Refraction.  —  The  earth  is  completely  sur- 
rounded  by   a   gaseous    medium   called   the  atmosphere. 

Even  when  perfectly  tran- 
quil, the  atmosphere  has 
a  remarkable  effect  upon 
the  motion  of  a  ray  of 
light  in  bending  it  out  of 
its  course.  Two  proper- 
ties true  of  all  gases  are 
concerned  in  atmospheric 
refraction  —  weight  and 
compressibility.  The  atmosphere  is  probably  at  least  100 
miles  in  depth ;  and  gravity  attracts  every  portion  of  it 
vertically  downward.  Its  total  weight  is  about  5  x  io15 
(five  quadrillions  =  5,000,000,000,000,000)  tons,  or  j2  O^CRTO 
that  of  the  entire  earth.  Conceive  the  atmosphere  divided 
into  layers  concentric  round  the  earth  and  one  another, 
as  above.  The  lowest  shell  must  support  not  only  the 
weight  of  the  shell  next  outside  it,  but  of  all  the  other 
shells  still  beyond.  Evidently,  then,  as  the  atmosphere 
is  compressible,  the  force  of  gravity  renders  successive 


Refraction  increases  the  Apparent  Altitude 


Law  of  Refraction 


strata  more  and  more  dense  as  the  surface  of  the  earth 
is  approached.  The  greater  the  density,  the  more  the  re- 
fraction ;  so  that  lower  strata  bend,  or  refract,  rays  of  light 
out  of  their  course  more  than  upper  layers  do. 

Law  of  Refraction.  —  According  to  the  law  of  refraction, 
rays  of  light  from  any  celestial  body  striking  the  air  in  the 
direction  of  the  plumb-line, 
will  pass  downward  along 
that  line  undeviated  ;  but  any 
rays  impinging  on  the  atmos- 
phere otherwise  than  verti- 
cally —  that  is,  rays  from 
celestial  bodies  whose  zenith 
distance  is  not  zero  —  will  be 
refracted  more  and  more 
from  their  original  course, 
the  nearer  they  are  to  the 
horizon.  The  less  the  alti- 
tude, the  greater  the  refrac- 
tion ;  and,  as  an  object  always  seems  to  be  in  that  direc- 
tion from  which  its  rays  enter  the  eye,  refraction  elevates 
the  heavenly  bodies,  or  makes  their  apparent  altitude 
greater  than  their  true  altitude.  The  figure  shows  how 
refraction  varies  from  zenith  to  horizon. 

If  the  altitude  is  45°,  the  refraction  is  58",  or  nearly  one  minute  of 
arc ;  but  so  rapidly  does  the  density  of  the  atmosphere  increase  near 
the  earth's  surface  that  the  refraction  at  zenith  distance  85°  is  9'  46", 
more  than  10  times  greater  than  at  45°;  and  increase  in  the  next  five 
degrees  is  even  more  rapid,  so  that  the  refraction  at  the  horizon  is 
34'  54".  A  correction  on  account  of  refra'ction  must  be  calculated 
and  applied  to  nearly  all  astronomical  observations.  Generally  ther- 
mometer and  barometer  must  both  be  read,  because  cold  air  is  denser 
than  warm,  and  a  high  barometer  indicates  increase  of  pressure  of  the 
superincumbent  air.  In  both  these  instances  the  amount  of  refraction 
is  increased.  To  determine  how  much  the  refraction  was  at  the  time 
when  an  astronomical  observation  was  made  at  a  given  altitude,  and  to 


Refraction  at  Different  Altitudes 


92  The  Earth  as  a  Globe 

apply  the  corresponding  correction  suitably,  is  part  of  the  work  of  the 
practical  astronomer.  It  is  greatly  facilitated  by  means  of  elaborate 
Refraction  Tables. 

Effects  of  Atmospheric  Refraction.  —  The  angular  breadth 
of  the  sun  is,  as  we  shall  see,  about  one  half  a  degree ;  and 
as  this  is  nearly  the  amount  of  atmospheric  refraction  at 
the  horizon,  evidently  the  sun  is  really  just  below  the  sensi- 
ble horizon  when  at  its  setting  we  still  see  it  just  above 
that  plane.  And  as  the  diurnal  motion  of  the  celestial 
sphere  carries  the  sun  over  its  own  breadth  in  about  two 
minutes  of  time,  refraction  lengthens  the  day  about  four 
minutes,  in  the  latitude  of  the  United  States ;  this  effect 
being  much  increased  as  higher  latitudes  are  reached.  It 
is  easy  to  see,  also,  that  the  sun  must  be  continually 
shining  on  more  than  an  exact  half  of  the  earth,  refrac- 
tion adding  a  zone  about  40  miles  wide  extending  all  the 
way  round  our  globe,  and  joining  on  the  line  of  sunrise 
and  sunset.  Farther  effects  of  atmospheric  refraction  are 
apparent  in  those  familiar  distortions  of  the  sun's  disk 
often  seen  just  before  sunset.  Refraction  elevates  the 
lower  edge,  or  limb,  more  than  the  upper  one,  so  that 
the  sun  appears  decidedly  flattened  in  figure,  its  vertical 
diameter  being  much  reduced  —  an  effect  far  more  pro- 
nounced in  winter  than  in  summer. 

Scintillation  of  the  Stars.  —  Scintillation  or  twinkling 
of  the  stars  is  a  rapid  shaking  or  vibration  of  their  light, 
caused  mainly  by  the  state  of  the  atmosphere,  though 
partly  as  a  result  of  the  color  of  their  intrinsic  light. 
That  the  atmosphere  is  a  cause  of  twinkling  is  evident 
from  the  fact  that  stars  twinkle  more  violently  near  the 
horizon,  where  their  rays  come  to  us  through  a  greater 
thickness  of  air. 

Also  the  stars  twinkle  more  in  winter  than  in  summer  ;  and  very  vio- 
lent scintillations  often  afford  a  good  forecast  of  rain  or  snow.  Marked 


Twilight 


93 


twinkling  of  the  stars  is  an  indication  that  the  atmosphere  is  in  a  state 
of  turmoil  —  currents  and  strata  of  different  temperatures  intermingling 
and  flowing  past  one  another.  The  astronomer  describes  this  state  of 
things  by  saying  that  the  'seeing  is  bad.'  Consequently,  high  magni- 
fying powers  cannot  be  advantageously  used  with  the  telescope.  A 
star's  light  seems  to  come  from  a  mere  point,  so  that  when  its  rays  are 
scattered  by  irregular  refraction,  at  one  instant  very  few  rays  reach  the. 
eye,  and  at  another  many.  This  accounts  for  the  seeming  changes  of 
brightness  in  a  twinkling  star.  Ordinarily  the  bright  planets  are  not 
seen  to  twinkle,  because  of  their  large  apparent  disks,  made  up  of  a 
multitude  of  points,  which  therefore  maintain  a  general  average  of 
brightness.  At  a  given  altitude  white  or  blue  stars  (Procyon,  Sirius, 
Vega)  twinkle  most,  yellow  stars  (Capella,  Pollux,  Rigel)  a  medium 
amount,  and  red  stars  (Aldebaran,  Antares,  Betelgeux)  least. 

Twilight.  —  At  a  particular  and  definite  instant  of  con- 
tact with  the  sensible  horizon,  the  sun's  upper  edge  comes 
into  view  at  sunrise  and  disappears  at  sunset.      But  long 
before  sunrise,  and 
a  corresponding 
time    after    sunset, 
there  is  an  indirect 
and   incomplete   il- 
lumination diffused 
throughout   the  at- 
mosphere.    This  is 
called    twilight. 
Morning  twilight  is 

generally  called  dawn.  In  part  twilight  is  due  to  sunlight 
reflected  from  the  upper  regions  of  the  earth's  atmosphere. 
As  twilight  lasts  until  the  sun  has  sunk  18°  below  the 
horizon,  evidently  its  duration  in  ordinary  latitudes  must 
vary  considerably  with  the  season  of  the  year.  But  the 
variation  dependent  upon  latitude  itself  is  greater  still. 
A  vast  twilight  zone  nearly  1500  miles  wide  completely 
encircles  the  earth. 

This  zone,  ABEF'm  the  figure,  is  continually  slipping  round  as  our 
globe  turns  on  its  axis.     One  edge  of  it,  along  the  line  of  sunrise  and 


The  Zone  of  Twilight  in  Midwinter 


94  The  Earth  as  a  Globe 

sunset,  is  constantly  facing  the  sun.  At  the  equator,  where  the  sun's 
daily  path  is  perpendicular  to  the  horizon,  the  earth  turns  through  this 
zone  of  twilight  in  about  i]  hours.  In  the  latitude  of  the  United  States, 
the  average  length  of  twilight  exceeds  i£  hours,  its  duration  being 
greatest  in  midsummer,  when  it  is  more  than  two  hours.  At  the 
actual  poles  of  the  earth,  twilight  is  about  2\  months  in  duration.  If 
Jlhe  earth  had  no  atmosphere,  there  would  be  no  twilight ;  the  blackness 
of  night  would  then  immediately  follow  the  setting  of  the  sun. 

The  Aurora.  —  The  aurora  borealis  (often  called  the 
northern  lights)  is  a  beautiful  luminosity,  striated  and 
variable,  seen  at  irregular  intervals,  and  only  at  night. 
From  the  general  latitude  of  the  United  States,  it  appears 
as  a  soft  vibrating  radiance,  streaming  up  most  often  into 
the  northern  sky,  occasionally  as  far  as  the  zenith,  but 
usually  in  a  semicircle  or  arch  extending  upward  not  over 
30°.  Its  probable  average  height  is  about  75  miles.  The 
aurora,  generally  greenish  yellow  in  color,  has  occasionally 
been  seen  of  a  deep  rose  hue,  as  well  as  of  a  pale  blue,  and 
other  tints.  The  continual  vibration,  sometimes  the  rapid 
pulsation,  of  its  streamers,  gives  it  a  character  of  mystery 
only  too  well  enhanced  by  our  lack  of  knowledge  of  its 
causes.  That  these  are  connected  with  the  magnetism 
of  the  earth  is  certain ;  also  that  a  strong  influence  upon 
the  magnetic  needle  is  somehow  exerted.  Telegraph  in- 
struments and  all  other  magnetic  apparatus  are  greatly 
disturbed  when  auroras  are  brightest.  This  wonderful 
spectacle  grows  more  frequent  and  pronounced,  as  the 
north  pole  is  approached ;  and  is  closely  connected,  though 
in  a  manner  incompletely  understood,  with  the  period  of 
sun  spots,  and  the  protuberances.  When  there  are  many 
sun  spots,  auroras  are  most  frequent  and  intense.  Proba- 
bly they  are  merely  an  electric  luminosity  of  very  rare 
gases. 

The  spectrum  of  the  aurora  is  discontinuous  (page  272),  and  far 
from  uniform.  Always  there  is  one  characteristic  green  line,  all  others 


The   Wandering  Terrestrial  Poles  95 

being  faint,  and  varying  from  one  auroral  display  to  another.  At  times 
there  appear  to  be  two  superposed  spectra.  A  similar  phenomenon  in 
the  southern  hemisphere  is  sometimes  called  aurora  australis ;  also  the 
general  term  aurora  polaris  is  often  applied  to  the  aurorae  of  both 
hemispheres. 

The  Wandering  Terrestrial  Poles.  —  Referring  back  to 
the  remarkable  photograph  of  stars  around  the  northern 
celestial  pole  (page  33),  we  recall  the  fact  that  the  center 
of  all  these  arcs  is  that  pole  itself.  And  we  may  farther 
define  the  terrestrial  north  pole  as  that  point  in  the  earth 
directly  underneath  this  celestial  pole,  or  that  point  on  our 
globe  where  the  center  of  this  system  of  concentric  arcs 
would  appear  to  be  exactly  in  the  zenith.  But  without 
actually  going  there,  how  can  astronomers  determine  the 
precise  position  of  this  point  on  the  earth's  surface,  and  so 
find  out  whether  it  shifts  or  not  ?  Evidently  by  finding  as 
closely  as  possible,  at  frequent  intervals  of  time,  the  lati- 
tude of  numerous  places  widely  scattered  over  the  world. 
If  the  latitude  of  a  place,  Berlin,  for  example,  is  found  to 
increase  slightly,  while  that  of  another  place  on  the  oppo- 
site side  of  the  globe,  as  Honolulu,  decreases  at  the  same 
time  and  by  the  same  amount,  the  inference  is  that  the 
position  of  the  earth's  axis  changes  slightly  in  the  earth 
itself.  So  definite  are  the  processes  of  practical  astronomy 
that  the  position  of  the  north  pole  can  be  located  with  no 
greater  uncertainty  than  the  area  of  a  large  Eskimo  hut. 
Nearly  all  the  great  observatories  of  the  world  are  fully 
3000  miles  from  this  pole ;  still  if  this  important  point 
should  oscillate  in  some  irregular  fashion  by  even  so  slight 
an  amount  as  three  or  four  paces,  the  change  would  be 
detected  at  these  observatories  by  a  corresponding  change 
in  their  latitude.  Such  a  fluctuation  of  the  pole  has  actu- 
ally been  ascertained,  and  it  affects  a  large  mass  of  the 
observations  of  precision  which  astronomers  and  geode- 


The  Earth  as  a  Globe 


sists  have  made  in  the  past. 
variation  of  latitude. 


Technically  it  is  called  the 


Only  recently  recognized,  the  physical  cause  of  it  is  not  yet  fully  es- 
tablished. But  the  nature  and  amount  of  it  are  already  pretty  well  made 
out.  Around  a  central  point  adjacent  to  the  earth's  north  pole,  draw  a 
circle  70  feet  in  diameter,  as  shown  in  the  illustration.  Within  this  cir- 
cle the  pole  has  always  been  since  the  beginning  of  1890.  Its  wander- 
ings from  that  time  onward  to  the  beginning  of  1895  are  clearly  indicated 

by  the  irregularly  curved 
line  which  has  been  care- 
fully laid  down  from  a 
discussion  of  a  large 
number  of  accurate  ob- 
servations of  latitude  at 
13  observatories  located 
in  different  parts  of  the 
world.  Let  the  eye  trace 
the  curve  through  all  its 
windings,  and  the  mean- 
ing of  the  oscillation,  or 
wandering  of  the  north 
pole,  will  be  appreciated. 
From  the  beginning  of 
1890  to  January,  1894, 
the  curve  seems  to  have 
been  roughly  an  in-wind- 

Observed  Wandering  of  the  North  Pole  ing  spiral,  the  pole  going 

round  once  in  about  14 

months.  The  latitudes  of  all  places  on  the  globe  change  by  corre- 
sponding amounts.  Chandler  of  Cambridge  first  brought  clearly  to 
light  the  variation  of  latitude,  and  American  investigation  of  it  has 
been  farther  advanced  by  Preston,  Doolittle,  and  Rees.  This  move- 
ment of  the  pole  is  not  yet  well  enough  understood  to  enable  astrono- 
mers to  predict  its  future  movements  ;  but  it  seems  probable  that  they 
will  be  confined  within  the  narrow  limits  here  indicated. 

Were  the  earth  at  perfect  rest  in  space,  its  poles  would 
not  partake  of  this  remarkable  motion,  in  part  dependent 
upon  a  slow  turning  round  on  its  axis.  The  next  chapter 
is  concerned  with  this  fundamental  relation,  of  the  utmost 
significance  in  astronomy,  both  theoretic  and  practical. 


CHAPTER   VI 

THE   EARTH   TURNS   ON   ITS  AXIS 

SO  far  we  have  dealt  only  with  the  seeming  motions  of 
the  heavenly  bodies  about  us ;  in  ancient  times  these 
were  regarded  as  their  actual  motions.  The  glory 
of  the  sun  by  day,  and  all  the  magnificence  of  the  nightly 
firmament  were  considered  accessory  to  the  earth  on  which 
men  dwell.  Till  the  time  of  Copernicus  our  abode  was 
generally  believed  to  be  enthroned  at  the  center  of  the 
universe.  Now  we  know,  what  is  far  less  gratifying  to  our 
self-importance,  that  this  earth  is  only  one  —  a  very  small 
one,  too  —  of  the  vast  throng  of  celestial  bodies  scattered 
through  space,  somewhat  as  moving  motes  in  a  sunbeam. 
All  the  stately  phenomena  of  the  diurnal  motion,  the 
appearances  we  have  been  studying,  are  easily  and  natu- 
rally explained  by  the  simple  turning  completely  round 
of  our  little  earth  on  its  axis  once  in  a  given  period  of 
time.  This  the  ancient  world  naturally  divided  unevenly 
into  day  and  night ;  but  the  astronomers  of  a  later  day, 
more  philosophically,  divide  it  into  24  hours,  all  of  equal 
length,  and  this  division  is  the  only  one  recognized  at  the 
present  day. 

In  the  Dome  of  the  Capitol.  —  Imagine  yourself  in  the  rotunda,  or 
directly  under  the  center  of  the  dome  of  the  Capitol  at  Washington. 
Turn  once  completely  round  from  right  to  left,  meanwhile  observing 
the  apparent  changes  in  the  objects  and  paintings  on  the  inner  walls  of 
the  dome.  Just  above  the  level  of  the  eye,  you  face,  one  after  another, 
all  the  twelve  historical  paintings  exhibited  in  the  rotunda.  Turning 
TODD'S  ASTRON.  —  7  97 


98  The  Earth   Turns  on  its  Axis 

round  again  at  the  same  speed  as  before,  the  pillars  half  way  up,  appar- 
ently much  reduced  in  size  from  their  greater  distance,  seem  to  move 
more  slowly.  Turning  round  the  third  time,  with  the  eyes  directed 
still  higher,  the  outer  figures  in  the  colossal  painting  at  top,  the  ceil- 
ing of  the  dome,  appear  to  turn  more  slowly  still ;  while  if  you  watch 
attentively  the  very  apex  of  the  dome,  the  central  point  of  Constantio 
Brumidrs  famous  fresco  will  seem  to  have  no  motion  whatever.  This 
very  simple  experiment  can  be  tried  quite  as  effectively  in  the  middle 
of  any  ordinary  square  room,  first  imagining  its  corners  drawn  inward, 
roughly  to  represent  a  dome.  Seat  yourself  on  a  revolving  piano  stool 
or  a  swivel  chair,  and,  as  you  turn  slowly  round  from  right  to  left,  watch 
the  apparent  motion  of  pictures  on  the  wall,  figures  in  the  frieze,  and 
spots  on  the  ceiling.  To  confine  the  direction  of  vision  look  through 
a  pasteboard  roll,  or  other  handy  tube,  elevating  it  to  different  alti- 
tudes as  desired.  Now  it  would  be  ridiculous  to  insist  that  the  dome 
(or  even  the  room)  is  turning  around  you,  thereby  causing  these 
changes,  while  you  are  at  rest  in  the  center.  Yet  this  was  precisely 
the  explanation  of  the  apparent  movement  of  the  heavens  accepted 
by  the  ancient  world,  false  as  it  was,  and  very  improbable  as  it  would 
in  our  age  seem  to  be.  While  the  true  doctrine  of  the  rotation  of  the 
earth  was  held  and  taught  by  a  few  philosophers  from  very  early  times, 
it  was  not  universally  accepted  till  the  downfall  of  the  Ptolemaic  system. 

The  Direction  in  which  the  Earth  turns.  —  When  riding 
swiftly  through  the  street  in  a  carriage  or  a  car,  it  is  quite 
easy,  by  imagining  yourself  at  rest,  to  see,  or  seem  to  see, 
all  the  fixed  objects  —  houses,  shops,  lamp-posts,  and  so 
on  —  rushing  by  just  as  swiftly  in  the  opposite  direction. 
Although  you  may  be  going  east,  you  seem  to  be  station- 
ary, and  they  appear  to  travel  west.  While  looking  at  the 
paintings  in  the  Capitol  (or  the  engravings  on  the  wall)  in 
succession  as  you  turned  round  from  right  toward  left,  they 
appeared  to  be  going  just  opposite  —  from  left  toward  right. 
Now  simply  conceive  all  these  objects  to  be  moved  outward 
in  straight  lines  from  the  point  of  observation,  each  in  the 
direction  in  which  it  lies,  to  a  distance  indefinitely  great 
as  if  along  the  spokes  of  a  vast  wheel,  whose  hub  is  at  the 
eye,  but  whose  tire  reaches  round  the  heavens.  When  re- 
moved to  a  distance  sufficiently  great,  we  may  imagine  them 


The  Earth   Turns  Eastward  99 

to  occupy  places  in  the  sky  which  some  of  the  celestial 
bodies  do.  But  we  have  seen  that  sun,  moon,  and  stars  all 
move  in  general  from  east  to  west,  so  we  reach  the  easy 
and  natural  conclusion  that  our  earth  is  turning  over  from 
west  toward  east.  Once  this  cardinal  fact  of  the  earth's 
turning  eastward  on  its  axis  is  established  and  accepted, 
there  is  a  full  explanation  of  that  apparent  westward  drift 
of  which  all  the  heavenly  bodies,  sun,  moon,  and  stars  in 
common,  partake.  Also  the  natural  succession  of  day  and 
night  is  robbed  of  its  ancient  mystery. 

Proof  that  the  Earth  turns  Eastward.  —  Quite  independently  of 
its  point  of  suspension,  a  pendulum  tends  to  swing  always  in  that  plane 
of  oscillation  in  which  it  is  originally  set  going.  Suspend  any  con- 
venient object,  weighing  one  or  two  pounds,  by  a  fine  thread  attached 
to  the  center  of  a  stick  or  ruler.  Hold  it  in  both  hands,  and  set  the 
pendulum  swinging  in  the  plane  of  the  stick.  Then,  without  raising 
or  lowering  it,  quickly  swing  the  ruler  quarter  way  round  its  center  in  a 
horizontal  plane.  The  pendulum  keeps  on  swinging  in  the  same  plane 
as  before,  although  it  is  now  at  right  angles  to  the  ruler.  Repeat  the 
experiment  several  times,  until  you  succeed  in  moving  the  stick  without 
changing  the  position  of  its  center,  and  it  will  be  seen  that  the  ruler 
may  be  swung,  either  slowly  or  rapidly,  into  any  position  whatever, 
without  affecting  the  plane  of  the  pendulum's  motion  appreciably. 
Now  imagine  the  short  thread  replaced  by  a  very  fine  wire  200  feet 
long,  suspending  a  ball  weighing  70  or  80  pounds  ;  and  in  place  of  the 
ruler  turned  round  by  hand  substitute  the  Panthe'on  at  Paris,  turned 
slowly  round  in  space  by  the  earth  itself.  These  are  the  conditions  of 
this  celebrated  experiment  as  tried  in  1851  by  Foucault,  a  French 
physicist,  who  thereby  provided  ocular  proof  that  the  earth  turns 
round  from  west  toward  east.  He  set  the  pendulum  swinging  in  the 
plane  of  the  meridian,  but  it  did  not  long  remain  so.  The  south  end 
of  the  floor  being  nearer  the  equator  than  the  north  end,  it  traveled 
eastward  a  little  faster  than  the  north  end  did,  so  that  the  floor  turned 
counter-clockwise  underneath  the  swinging  pendulum.  Therefore,  the 
plane  of  oscillation  appeared  to  swing  round  clockwise.  This  experi- 
ment has  been  repeated  in  different  parts  of  the  earth,  and  always  with 
the  same  resm"t.  The  four  figures  on  the  next  page  show  the  varying 
conditions.  In  the  southern  hemisphere  the  pendulum  appears  to  turn 
round  counter-clockwise.  As  for  the  rate  of  turning,  at  either  pole  it 
makes  a  complete  revolution  in  the  same  time  that  the  earth  does,  and 


IOO 


The  Earth   Turns  on  its  Axis 


the  time  of  revolution  grows  greater  and 
greater  as  the  latitude  grows  less.  Exactly 
on  the  equator,  the  plane  of  oscillation  does 
not  change  at  all  with  reference  to  the 
meridian. 


In  Northern  Latitudes 


In  Southern   Latitudes 


Day  and  Night.  —  Granted  the 
rotation  of  the  earth  on  its  axis,  and 
the  alternation  of  day  and  night  is 
fully  and  clearly  explained.  The 
sun  may  even  remain  fixed  among 
the  stars  of  the  celestial  vault.  By 
the  earth's  turning  round,  all  places 
upon  its  surface,  as  New  York, 
Chicago,  and  San  Francisco,  are 
carried  into  the  sunshine  and  out 
of  it  alternately.  From  the  dark- 
ness of  night  there  comes,  first,  the 
dawn,  with  twilight  growing  brighter 
and  brighter,  then  sunrise,  followed 
by  the  sun  rising  higher  and  higher, 
till  it  reaches  the  meridian.  Then 
it  is  midday,  or  noon.  Afterward 
the  order  of  occurrence  is  reversed, 
—  noon,  afternoon,  sunset,  twilight, 
night  again.  All  these  phenomena 
are,  in  a  general  way,  connected 
by  everybody  with  lapse  of  time,  and 
progress  of  the  hours  from  night  to 
noon,  and  from  noon  back  to  night 
again.  Uniform  turning  of  the  globe 
in  the  figure  opposite  mak^s  this  rela- 
tion obvious.  Count  of  the  hours 
At  the  Equator  is  begun  at  o  or  12,  when  the  sun  is 

Foucauit's  Experimental  Proof    highest,  and  continued  to  12,  when 

of  Earth's  Rotation  B 


At  the  North  Pole 


Day  and  Night  at  the  Equinoxes          101 

the  sun  is  lowest;  and  if  earth  were  transparent  as  crystal, 
the  sun  could  be  seen  through  it  from  sunset  to  sunrise — 
crossing  the  lower  meridian  directly  underneath  the 
northern  horizon  at  midnight. 

Day  and  Night  at  the  Equinoxes.  —  The  ecliptic  has 
been  denned  as  the  yearly  path  of  the  sun  round  the 
heavens.  As  it  lies  at  an  angle  of  23^-°  to  the  celestial 
equator,  at  some  time  each  year  the  sun's  declination 
must  be  23^°  south,  and  six  months  from  that  time 
its  declination  must  be  23^°  north.  Midway  between 


Alternation  of  Day  and  Night 

these  points,  the  sun  will  be  crossing  the  equator; 
that  is,  its  declination  will  be  zero,  and  the  sun's  center 
will  be  at  those  points  of  intersection  of  equator  and 
ecliptic,  called  the  equinoxes.  Why  they  are  so  called 
will  be  apparent  from  the  figure  above  given ;  for  the 
sun  is  on  the  celestial  equator,  because  the  earth's  equa- 
tor-plane extended  would  pass  through  it.  The  great  cir- 
cle of  the  globe  which  separates  the  day  hemisphere  from 
the  night  hemisphere,  exactly  coincides  with  a  terrestrial 
meridian.  Everywhere  on  that  meridian  it  is  6  o'clock 
—  6  o'clock  A.M.  on  the  half  which  the  globe  by  its  turn- 
ing is  carrying  round  toward  the  sun,  and  6  o'clock  P.M. 
on  the  other  half  which  is  being  carried  out  of  sunlight. 


IO2 


The  Earth   Turns  on  its  Axis 


S.P. 


It  is  sunrise  everywhere  on  the  former  half  of  this  meridian, 
and  sunset  everywhere  on  the  latter  half.  As  daytime  is 
the  interval  from  sunrise  to  sunset,  and  night-time  is  the 
interval  from  sunset  to  sunrise,  the  day  and  the  night  are 
each  12  hours  in  length,  and  therefore  equal.  Whence 
the  term  equinox,  from  the  two  Latin  words  that  give  us 
our  English  words  equal  and  night.  This  equality  of  day 

and  night  all  over  the 
world  occurs  only  twice 
each  year.  When  the  sun 
is  crossing  the  equator  and 
going  northward,  this  hap- 
pens about  the  2ist  of 
March ;  and  going  south- 
ward, about  the  2ist  of 
September. 

Day  and  Night  at  the 
Solstices.  —  From  March  to 
September,  the  sun  is  north 
of  the  celestial  equator.  Therefore,  at  our  middle  lati- 
tudes he  is  among  the  stars  that  are  above  the  horizon 
longer  than  they  are  below  it,  as  the  upper  figure  on 
page  72  clearly  shows.  During  this  period  of  the  year, 
daytime  in  north  latitudes  is  always  longer  than  the  night- 
time immediately  preceding  or  following  it.  At  the  sum- 
mer solstice  the  sun's  declination  has  reached  its  maximum, 
or  23^°.  The  days  then  will  be  as  long  as  possible,  and  the 
nights  as  short  as  possible.  From  September  to  March,  on 
the  other  hand,  the  sun  is  south  of  the  celestial  equator,  and 
therefore  among  the  stars  that  are  below  the  horizon  longer 
than  they  are  above  it.  During  these  months,  then,  night- 
time in  our  hemisphere  is  always  longer  than  daytime.  At 
the  winter  solstice  the  sun's  declination  is  again  a  maximum, 
but  it  is  23^°  south  or  about  midway  between  E  and  S.  So 


Diurnal  Circles  in  Middle  South  Latitudes 


Day  and  Night  at  Equator 


103 


that  the  days  are  then  shortest,  and  the  nights  longest.  But 
these  relations  of  day  and  night  to  the  different  months  are 
true  for  the  northern  hemisphere  only. 


Day  and  Night  South  of  the  Equator.  —  The  opposite  figure  has  been 
suitably  modified  from  the  one  on  page  72,  in  order  to  show  the  relation 
of  day  and  night  at  different  times  of  the  year  for  places  of  middle  south 
latitude.  By  holding  the  page  in  a  vertical  plane,  and  looking  west  as 
you  read,  the  diagrams  will  better  correspond  to  actual  conditions. 
For  every  degree  of  latitude  that  you  pass  over,  in  traveling  southward, 
the  north  pole  of  the  heavens  goes  down  one  degree,  and  the  south 
pole  rises  one  degree.  The  diagram  opposite  is  adapted  to  south  lati- 
tude 45°,  much  farther  south  than  either  Capetown,  Valparaiso,  or  Mel- 
bourne. The  south  pole  of  the  heavens  is  now  as  far  above  the  south 
horizon  as  it  was  below  the  south 
horizon,  in  a  place  of  equal  north  Q 

latitude;    and   the  relations    of  £iE 

daytime  to  night-time  are  corre- 
spondingly reversed.  From  Sep- 
tember to  March,  therefore,  when 
the  sun's  declination  is  south,  the 
sun  is  among  the  stars  that  are 
above  the  horizon  longer  than 
they  are  below  it;  so  that  the 
daytime  always  exceeds  the 
night.  From  March  to  Sep-  s 
tember,  the  sun  being  in  north 
declination,  the  daytime  clearly 
is  shorter  than  the  night.  If  at 
any  time  of  the  year  we  com- 
pare the  length  of  the  day  at  a 
given  north  latitude  with  the 
length  of  the  night  at  an  equal 
south  latitude,  we  shall  find  them 
equal.  Also  the  converse  of  this 
proposition  is  true. 

Day  and  Night  at  the  Earth's  Equator.  —  We  have  considered  the 
relation  of  day  to  night  at  middle  north  latitudes  ;  and  the  explanation 
given  holds  good  for  all  places  in  the  United  States.  Also  the  oppo- 
site relations,  which  obtain  in  south  latitudes.  It  remains  to  consider 
the  effect  at  the  equator.  Recalling  the  fact  that  the  latitude  of  a 
place  is  always  equal  to  the  altitude  of  the  visible  pole  of  the  heavens, 
it  is  clear  that  if  the  place  selected  is  anywhere  on  the  earth's  equator, 


Diurnal  Circles  at  the  Equator 


IO4  The  Earth   Turns  on  its  Axis 

both  celestial  poles  must  be  visible  and  coincide  with  the  north 
and  south  points  of  the  horizon  (figure  on  preceding  page).  The 
horizon,  then,  must  coincide  with  the  celestial  meridians,  or  hour  circles, 
one  after  another  as  they  seem  to  pass  by  it,  in  consequence  of  the 
apparent  motion  of  the  celestial  sphere ;  and  every  star's  diurnal  circle 
is  the  same  as  its  parallel  of  declination.  But  every  hour  circle  divider 
parallels  of  declination  in  half;  therefore,  every  star  of  the  celestial 
sphere,  as  seen  from  a  station  on  the  earth's  equator,  is  above  the 
horizon  12  hours  and  below  it  12  hours.  Clearly  this  is  true  no 
matter  what  the  star's  declination  may  be ;  therefore  it  must  always  be 
true  of  the  sun,  although  its  declination  is  all  the  time  changing.  Had 
the  early  peoples  who  invented  our  astronomical  terms  lived  upon  the 
equator  where  day  and  night  are  always  equal,  the  term  equinox  would 
not  have  signified  anything  unusual,  and  a  different  word  would  have 
been  necessary  to  define  the  time  when,  and  the  point  where,  the  sun 
crosses  the  celestial  equator. 

Sunrise  and  Sunset.  —  Refer  to  any  ordinary  almanac. 
The  times  of  sunrise  and  sunset  are  given  usually  for  two 
or  three  definite  cities,  north  and  south,  or  for  zones  of  states 
varying  widely  in  latitude.  These  are  local  mean  times 
when  the  upper  edge  or  limb  of  the  true  sun,  as  corrected 
for  refraction,  is  in  contact  with  the  sensible  horizon  of 
the  place,  or  of  any  place  of  equal  latitude.  The  local 
time  will  not  often  coincide  with  the  standard  time,  now 
almost  universally  used.  But  the  correction  required  is 
simply  dependent  upon  the  difference  between  the  longi- 
tudes of  the  place  and  of  the  standard  meridian.  If  you 
are  west  of  the  standard  meridian,  for  each  degree  add 
four  minutes  to  the  almanac  times ;  if  east,  subtract.  In 
verifying  the  almanac  times  by  observation,  remember  the 
difference  between  sensible  and  apparent  horizons. 

Almanac  Sunrise  and  Sunset  at  the  Equinoxes.  —  We  have  seen 
that  when  the  sun  — that  is,  the  sun's  center — is  on  the  equator,  it  rises 
at  the  same  time  everywhere,  and  that  time  is  6  o'clock.  So,  too,  it  sets 
everywhere  at  6  o'clock.  Why,  then,  do  the  times  predicted  in  the 
almanacs  differ  from  this?  The  reason  is  threefold,  (a}  The  times  of 
sunrise  and  sunset  are  all  corrected  for  refraction,  which  at  the  horizon 
amounts  to  nearly  o°.6,  or  more  than  the  sun's  own  breadth.  As  re- 


The  Midnight  Sun  105 

fraction  always  increases  the  apparent  altitude  of  celestial  bodies, 
the  sun  can  be  seen  wholly  above  the  horizon  when  really  below  it. 
Therefore  this  effect  alone  lengthens  the  daytime  about  five  minutes, 
causing  the  refracted  sun  to  rise  about  two  and  one  half  minutes  earlier 
than  the  true  sun,  and  set  about  the  same  amount  later,  (b}  The 
almanac  times  of  sunrise  and  sunset  refer  to  the  upper  edge  or  limb  of 
the  sun.  not  the  center.  Here,  again,  is  a  cause  operating  in  like  man- 
ner with  the  refraction,  but  with  an  effect  about  half  as  great,  (c)  The 
almanac  times  are  mean  solar  times  of  the  rising  and  setting  of  the  real 
sun.  This  difference  between  true  sun  and  fictitious  sun  also  displaces 
the  times  of  sunrise  and  sunset,  by  the  amount  of  the  equation  of  time 
(page  112):  at  the  vernal  equinox  the  sun  is  six  minutes  slow ;  at  the 
autumnal  equinox,  eight  minutes  fast.  All  three  effects  when  combined 
at  the  vernal  equinox,  delay  the  sunset  until  long  after  six.  and  cause 
the  sun  to  rise  at  the  autumnal  equinox  long  before  six. 

Sunrise  and  Sunset  in  Different  Latitudes.  —  Compare 
the  almanac  times  of  sunrise  and  sunset  in  different  lati- 
tudes on  the  same  day.  At  the  end  of  the  third  week 
of  March,  the  times  of  sunrise  are  practically  the  same, 
no  matter  what  the  latitude.  So  are  the  sunset  times. 
Through  April,  May,  and  June,  the  farther  north,  the 
earlier  is  sunrise  and  the  later  is  sunset;  the  daytime  is 
longer,  and  the  night-time  shorter.  This  difference  on 
account  -of  latitude  increases  until  the  third  week  in  June  ; 
then  it  slowly  diminishes  until  sunrise  and  sunset  again 
occur  at  the  same  time  regardless  of  latitude,  at  the  end  of 
the  third  week  in  September. 

Through  the  remaining  half  of  the  year,  a  change  of  latitude  affects 
the  time  of  sunrise  oppositely ;  also  the  time  of  sunset :  the  farther 
north  one  goes,  the  later  is  sunrise,  and  the  earlier  is  sunset.  The 
diytime  is  shorter,  and  the  night-time  longer.  As  the  year  wears  on, 
the  latitude-difference  of  the  times  of  both  sunrise  and  sunset  grows 
greater,  until  about  Christmas  time  ;  afterward  it  as  gradually  decreases 
until  the  vernal  equinox.  Then,  go  north  or  south  as  far  as  one  may 
choose,  the  sun  will  rise  at  the  same  local  time ;  and  sunset  will  be 
unaffected  also. 

The  Midnight  Sun.  —The  farther  north  one  travels,  the 
higher  the  pole  rises  toward  the  zenith ;  consequently  a 


io6 


The  Earth   Turns  on  its  Axis 


\      NORTHERN  HORIZON       / 


\ 


AT  WASHINGTOK 


IORTHERN  HORIZON 


HORIZON 
AT  ST.PETERSBURG 


Midsummer  Sun  at 
Midnight 


latitude  must  after  a  while  be  reached  where  the  midsum- 
mer sun,  at  and  near  the  solstice,  just  grazes  the  north 
horizon  at  midnight,  and  so  does  not  set 
at  all.  The  daytime  period,  therefore,  is 
24  hours  long,  and  night-time  vanishes. 
For  the  northern  hemisphere,  the  northern 
parallel  of  66^°  is  this  latitude.  The 
change  in  the  sun's  daily  path  will  be 
apparent  in  referring  to  the  illustration  ; 
it  shows  how  much  shorter  the  sun's  arc  of 
invisibility  below  the  horizon  grows,  as  one 
travels  north,  from  Washington  to  Paris, 
Saint  Petersburg,  and  Lapland.  Midnight 
sun  is  the  popular  name  for  the  sun  when 
visible  in  midsummer  at  its  lower  culmi- 
nation underneath  the  pole  of  the  heavens. 
The  entire  period  of  24  hours  is  all  daytime,  and  there  is 
no  night.  It  occurs  in  high  northern  latitudes  in  June ; 
and  similarly  in  high  southern  latitudes  in  December,  the 
midsummer  period  of  the  southern  hemisphere.  The 
northern  extremity  of  the  Scandinavian  peninsula  is  known 
as  the  '  Land  of  the  Midnight  Sun,'  because  this  weird  and 
unusual  phenomenon  has  been  most  often  observed  from 
that  region. 

Length  of  Day  at  Different  Latitudes.  —  For  all  places 
on  the  earth's  equator  there  is  never  any  inequality  of  day 
and  night.  The  farther  we  go  from  the  equator,  either 
north  or  south,  the  greater  this  inequality,  the  longer 
will  be  the  days  of  summer,  and  the  nights  of  winter. 
Regarding  the  day  geometrically  as  the  interval  of  time 
during  which  the  center  of  the  sun  is  above  the  sensible 
horizon,  it  is  easy  to  calculate  the  greatest  length  of  the  day 
at  any  given  latitude.  The  results  are  as  follows  and  they 
are  true  for  latitudes  either  north  or  south  of  the  equator : 


The  Long  Polar  Night  107 

MAXIMUM  LENGTH  OF  DAY  AT  DIFFERENT  LATITUDES 


AT  LATITUDE  — 

GREATEST  LENGTH  OF 
DAY  is  — 

AT  LATITUDE  — 

GREATEST  LENGTH  OF 
DAY  is  — 

o°.o 

12  h. 

Months 

30  .8 

14 

67°-4 

I 

49  -° 

16 

73  '7 

3 

58.5 

18 

84.1 

5 

63  -4 

20 

90  .0 

6 

65  .8 

22 

66.5 

24 

But  these  results  are  much  modified  by  refraction  of  the 
atmosphere.  At  the  time  of  greatest  length  of  day  in  the 
northern  hemisphere  is  occurring  the  greatest  length  of 
night  in  the  southern  hemisphere. 

The  Long  Polar  Night.  — Ordinary  notions  of  the  six  months  of  the 
polar  night  need  some  correction.  If  the  actual  north  pole  were  reached, 
it  is  true  that  the  sun  would  really  be  below  the  horizon  very  nearly 
six  months,  that  is  from  the  2oth  of  September  to  the  2oth  of  March, 
while  it  is  south  of  the  equator ;  and  imagining  the  earth  to  turn  round 
on  its  axis  inside  of  this  atmosphere  shell,  as  in  the  figure  on  page  93,  it 
is  clear  how  twilight  at  the  pole  under  B  continues  throughout  the  en- 
tire 24  hours,  so  long  as  the  pole  is  inclined  away  from  the  sun.  But 
the  duration  of  twilight,  longer  and  longer  as  the  pole  is  approached,  is 
a  very  important  factor  not  to  be  neglected.  Supposing  twilight  to  last 
till  the  sun  is  depressed  18°  below  the  horizon,  so  long  is  the  autumn 
twilight  that  its  continuance  for  2^  months  would  postpone  the  begin- 
ning of  deep  night  till  about  the  ist  of  December;  while  the  spring 
dawn,  equally  protracted,  would  begin  early  in  January.  Even  at  the 
pole,  then,  true  night  with  an  absolutely  dark  sky  would  be  only  six  or 
seven  weeks  long.  So  much  for  the  sun  ;  and  fortunately  for  the  arc- 
tic explorer,  the  moon  helps  wonderfully  to  alleviate  this  dreary  period. 
As  the  sun  is  so  far  south,  the  crescent  moon  at  old  and  new,  being 
near  it,  will,  like  the  sun  itself,  be  below  the  polar  horizon ;  but  during 
the  fortnight  from  first  quarter  to  last  quarter,  including  the  period  of 
its  full  phase,  it  will  shine  continually  above  the  horizon.  As  the  moon 
must  'full1  at  least  twice  during  the  \\  months  when  sunlight  is  wholly 
withdrawn,  the  period  of  absolute  night  is  reduced  to  about  three  weeks 


io8  The  Earth   Turns  on  its  Axis 

at  the  most.  And  even  this  will  now  and  then  be  broken  by  brilliant 
auroras,  especially  during  years  of  prevalent  sun  spots.  If  one  retreats 
from  the  pole  only  5°,  or  to  latitude  85°  north,  it  is  quite  possible  that 
the  period  of  utter  night  may  vanish  entirely ;  and,  of  course,  still  far- 
ther south,  the  number  of  hours  of  night  illumined  by  neither  sun  nor 
moon  must  usually  be  exceedingly  few. 

The  Sidereal  Day.  —  As  referred  to  a  fixed  star,  the 
period  of  rotation  of  the  earth  on  its  axis  does  not  vary. 
One  such  rotation  is  called  a  sidereal  day,  or  day  as  re- 
ferred to  the  stars.  It  is  subdivided  into  24  sidereal  hours, 
each  hour  into  60  sidereal  minutes,  and  each  minute  into 
60  sidereal  seconds.  Every  observatory  possesses  a  clock 
regulated  to  keep  this  kind  of  time,  and  called  a  sidereal 
clock.  The  hours  of  sidereal  time  are  always  counted 
consecutively  through  the  sidereal  day  from  o  to  24. 

Approximately  in  the  meridian,  as  found  from  the  sun  by  the  method 
on  page  23,  suspend  two  plumb-lines  from  some  rigid  support  which 
does  not  obstruct  the  view  south.  Secure  the  lower  ends  of  the  plumb- 
lines  in  the  exact  position  where  they  come  to  rest,  taking  care  to  stretch 
the  lines  taut.  As  soon  as  the  stars  are  out,  observe  and  record  the 
hour,  minute,  and  second  when  some  bright  star  is  in  .line  with  both  of 
them.  Its  altitude  should  not  exceed  60°  above  the  south  horizon. 
Use  the  best  clock  or  watch  at  hand.  The  next  clear  night,  repeat  the 
observation  on  the  same  star ;  also  on  two  succeeding  evenings,  setting 
down  the  day,  hour,  minute,  and  second  in  each  case,  and  taking  care 
that  the  running  of  the  timepiece  shall  not  be  interfered  with  mean- 
while, nor  the  plumb-lines  disturbed.  On  comparing  these  observa- 
tions it  will  be  found  that  the  star  has  been  crossing  the  plumb-lines 
about  four  minutes  earlier  each  day.  If  the  observations  were  to  be 
continued  on  subsequent  days,  we  should  find  only  the  same  result, 
and  so  on  indefinitely :  the  star  would  soon  come  to  the  lines  in  bright 
twilight,  and  it  could  not  be  observed  without  a  telescope.  A  few  days 
later  it  would  cross  at  sunset,  and  it  is  easy  to  calculate  that  in  about 
three  months  it  would  cross  at  noon,  star  and  sun  culminating  to- 
gether. By  this  simple  method  is  established  that  cardinal  element  in 
astronomy,  the  period  of  the  earth's  turning  round  on  its  axis.  Astrono- 
mers have,  to  be  sure,  much  more  accurate  methods  than  this ;  and  the 
instruments  employed  by  them  are  described  and  pictured  in  a  later 
chapter,  but  only  the  details  vary,  the  principle  remaining  the  same. 


Telling   Time  by  the  Stars 


109 


•0 


Telling  Time  by  the  Stars.  —  Our  next  inquiry  concerns 
the  point  that  corresponds  to  o  hours,  o  minutes,  o  seconds; 
that  is,  the  beginning  of  the  sidereal  day.  Having  found 
this,  our  timepiece 
may  be  set  to  corre- 
spond;  and  if  regu- 
lated, it  will  continue 
to  keep  sidereal  time. 
As  sidereal  time  sus- 
tains a  relation  to  the 
sun  which  is  all  the 
while  varying,  it  is 
clear  that  the  sidereal 
day  may  begin  when 
any  star  is  crossing 
the  meridian  ;  but  it 
is  also  clear  that  all 
astronomers  should 
agree  to  begin  the 
sidereal  day  by  one 
and  the  same  star,  or 
reference  point.  This  is  practically  what  they  have  done ; 
and  the  point  selected  is  the  vernal  equinox,  often  called 
'  the  First  of  Aries,'  or  '  the  First  point  of  Aries ' ;  also 
sometimes,  '  The  Greenwich  of  the  Sky.' 

The  equinoctial  colure  passes  through  it;  and  for  all  stars  exactly 
between  the  vernal  equinox  and  either  celestial  pole,  the  right  ascension 
is  zero,  no  matter  what  their  declination  may  be.  Fortunately  there  is 
a  bright  star  almost  on  this  line,  and  only  32°  from  the  north  pole ;  so 
it  is  always  above  the  horizon  in  our  country,  except  for  an  hour  or 
two  each  day.  in  some  of  the  most  southern  states.  This  important 
star  is  Beta  Cassiopeiae  (page  66).  When  it  is  crossing  the  upper  merid- 
ian, being  as  near  as  possible  to  the  zenith,  sidereal  time  is  o  h.  o  m  o  s. 
and  a  new  sidereal  day  begins.  The  relation  of  this  conspicuous  star  to 
Polaris  is  shown  in  the  above  diagram.  Surrounding  both  stars  is 
drawn  a  clock-hand  which  may  be  imagined  as  turning  round  with  the 


NORTH      e 


Telling  the  Sidereal  Time  by  Cassiopeia 


1 1  o  The  Earth   Turns  on  its  Axis 

stars  once  each  day.  Very  little  practice  is  necessary  to  enable  one  to 
tell  the  sidereal  time  by  the  direction  of  this  colossal  clock-hand  in  the 
northern  sky ;  but  one  must  never  fail  to  notice  that  it  moves  oppositely 
to  the  hour  hand  of  an  ordinary  watch,  and  only  half  as  fast.  At  6  h. 
it  points  toward  the  west  horizon,  and  at  18  h.  toward  the  east  point  of 
the  horizon ;  not  horizontally,  as  represented  in  the  figure,  but  down- 
ward in  each  case  by  a  considerable  angle  varying  with  the  latitude. 
Subtracting  the l  sidereal  time  of  mean  noon1  (page  122),  gives  ordinary 
or  solar  time.  This  operation  is  called  l  telling  time  by  the  stars 1  - 
a  method  of  course  only  approximate ;  but  an  error  greater  than  1 5 
or  20  minutes  will  not  often  occur. 

The  Apparent  Solar  Day.  —  It  was  shown  (page  108)  how 
to  ascertain  by  observation  that  the  sun  seems  to  be  con- 
tinually moving  eastward  among  the  stars.  It  was  shown, 
too,  that  sidereal  noon  (noon  by  the  stars)  comes  at  all 
hours  of  the  day  and  night  during  the  progress  of  the 
year.  Plainly,  then,  sidereal  time  is  not  a  fit  standard  for 
regulating  the  affairs  of  ordinary  life ;  for,  while  it  would 
answer  very  well  for  a  fortnight  or  so,  the  displacement  of 
four  minutes  daily  would  in  six  months  have  all  the  world 
breakfasting  after  sunset,  staying  awake  all  through  the 
night,  and  going  to  bed  in  the  middle  of  the  forenoon. 
As  the  sun  is  the  natural  time-regulator  of  the  engage- 
ments and  occupations  of  humanity,  he  is  adopted  as  the 
standard,  although  you  will  find  by  observing  attentively 
that  his  apparent  motion  is  beset  with  serious  irregulari- 
ties. Begin  on  any  day  of  the  year,  and  observe  the  sun's 
transit  of  the  meridian,  as  you  did  that  of  a  star.  The 
instant  when  the  sun's  center  is  on  the  meridian  is 
known  as  apparent  noon.  If  you  repeat  the  observation 
every  day  for  a  year,  and  then  compare  the  intervals 
between  successive  transits,  you  will  find  them  varying 
in  length  by  many  seconds,  because  they  are  all  apparent 
solar  days ;  they  will  not  all  be  equal,  as  in  the  case  of 
the  star. 

The  Mean  Solar  Day.  —  By  taking  the  average  of  all 


Astronomical  and  Civil  Day  1 1 1 

the  intervals  between  the  sun's  transits,  that  is,  the  mean 
of  all  apparent  solar  days  in  course  of  the  year,  an  invari- 
able standard  is  obtained,  like  that  from  the  stars  them- 
selves. In  effect,  this  is  precisely  what  astronomers  have 
done,  with  great  care  and  system;  and  for  convenience, 
they  imagine  an  average,  or  mean,  sun,  called  the  ficti- 
tious siui,  which  they  accept  as  their  standard,  and  then 
calculate  the  difference  between  its  position  and  that  of 
the  real  sun  which  they  observe.  The  fictitious  sun  may 
be  defined  as  an  imaginary  point  or  star  which  travels 
eastward  round  the  celestial  equator,  not  the  ecliptic,  at 
a  perfectly  uniform  rate,  making  the  entire  circuit  of  the 
heavens  in  course  of  the  year.  It  is  easy  to  see  that  the 
intervals  between  transits  of  the  fictitious  sun  must  all 
be  equal;  and  obviously,  too,  this  interval  is  longer  than 
the  sidereal  day,  for  this  reason :  if  a  star  and  the  ficti- 
tious sun  should  cross  the  meridian  together  on  one  day, 
then  on  the  next  day  the  star  would  come  to  the  merid- 
ian first,  thereby  making  the  sidereal  day  shorter  than 
the  solar  day.  The  instant  when  the  center  of  the  ficti- 
tious sun  is  on  the  meridian  is  called  mean  noon.  The 
mean  solar  day^ therefore,  may  be  defined  as  the  interval 
between  two  adjacent  transits  of  the  fictitious  sun  over  the 
same  meridian ;  or  the  mean  of  all  the  apparent  solar 
days  of  the  year.  It  is  divided  into  24  mean  solar  hours, 
each  hour  into  60  mean  solar  minutes,  and  each  minute 
into  60  mean  solar  seconds.  This  is  the  kind  of  hours, 
minutes,  and  seconds  kept  by  clocks  and  watches  in  com- 
mon use. 

Astronomical  and  Civil  Day. — The  mean  solar  day  is 
often  called  the  astronomical  day,  because  it  begins  at 
one  mean  noon  and  ends  at  the  one  next  following.  Its 
hours  are  counted  continuously  from  o  to  24,  without  a 
break  at  midnight.  It  is  the  day  recognized  by  astronomers 


1 1 2  The  Earth   Turns  on  its  Axis 

in  observatory  work  and  records,  and  by  navigators  in  using 
the  Nautical  Almanac.  The  ordinary  or  civil  day  is  ex- 
actly the  same  in  length  as  the  astronomical  day,  but  it 
begins  at  the-  midnight  preceding  noon  of  a  given  astro- 
nomical day,  and  ends  at  the  next  following  midnight.  As 
every  one  knows,  its  hours  are  not  usually  counted  con- 
tinuously from  o  to  24,  but  in  two  periods  of  12  each.  The 
hours  of  its  first  period  are  ante  meridiem,  that  is,  before 
midday,  or  A.M.,  and  the  hours  of  its  second  period  are 
post  meridiem,  that  is,  after  midday,  or  P.M.  Therefore, 
civil  time,  P.M.,  of  a  given  date  is  just  the  same  as  the 
astronomical  time ;  if  a  date  recorded  in  astronomical  time 
between  midnight  and  noon  is  to  be  converted  into  civil 
time,  it  is  necessary  to  subtract  12  from  the  hours  and  add 
i  to  the  days.  For  example  :  — 

CIVIL  DATE  ASTRONOMICAL 

6  o'clock  P.M.,  loth  November,  1899  =  1899  November  10  d.    6  h. 
3  o'clock  A.M.,  I5th  December,  1899  =  1899  December  14  d.  15  h. 

The  astronomical  date  is  always  recorded  in  the  philo- 
sophic order  here  given  —  year,  month,  day,  hour,  minute, 
second. 

The  Equation  of  Time.  —  Ordinary  clocks  and  watches 
are  regulated  to  run  according  to  the  average,  or  fictitious, 
sun,  which  makes  all  the  days  of  equal  length  ;  the  sun 
itself  is  sometimes  ahead  of  this  'fictitious  sun,'  and  some- 
times behind  it.  This  deviation  is  called  the  equation  of 
time,  and  the  explanation  of  it  is  given  in  the  next  chapter. 
We  shall  soon  need  it  (page  119)  in  ascertaining  mean 
noon  by  observing  the  real  sun's  transit  over  the  meridian. 
With  sufficient  accuracy  for  the  years  1897-1900  it  is  as 
follows :  S  meaning  '  sun  slow '  (that  is,  the  center  of  the 
real  sun  does  not  cross  the  meridian  until  after  mean 
noon),  and  F  meaning  '  sun  fast ' :  — 


Retardation  of  Sunset 
THE  EQUATION  OF  TIME 


| 

MONTH 

JANUARY 

FEBRUARY 

MARCH 

APRIL 

MAY 

JUNE 

m        s. 

m.         s 

m.        s. 

m.        s. 

m.         s 

m.        s 

I 

S    4       7 

Si3     54 

SI2       23 

S3     44 

F3       6 

F2       21 

6 

S    6     23 

S  14    21     S  ii     17 

82     16 

F3     34. 

F  i     29 

ii 

S    8     26    S  14     27 

S  10      o 

So     53 

F3     49 

Fo     31 

16 

S  10     14    S  14     14 

S    8     35 

Fo       22 

F3     49 

So     31 

21 

S  ii     44    S  13     43 

S    7       5 

F  i     29 

F3     36 

S  i     36 

26 

S  12     55     S  12     57 

S    5     34 

F2     24 

F3      9 

S  2      40 

31 

S  13     46 

Sn     58 

S   4      2 

F3       6 

F2     30 

S3     40 

MONTH 

JULY 

AUGUST 

SEPTEMBER 

OCTOBER 

NOVEMBER 

DECEMBER 

m.         s 

m.         s. 

m.        s. 

m.         s. 

m         s 

m.         s. 

I 

S3     40 

S6      4 

F   o     19 

F  10     32 

F  16     19 

F  10     32 

6 

S4     34 

S5     37 

F    i     57 

Fi2       3 

F  16     13 

F   8     30 

1  1 

85     18 

S4    55 

F    3     40 

Fi3     23 

Fi5     46 

F   6     16 

16 

S5     51 

S3     59 

F    5     25 

Fi4    3i 

Fi4     58 

F   3     52 

21 

S6     10 

82     50 

F    7     ii 

Fi5     24 

Fi3     49 

F    i     23 

26 

S6     16 

S  i     30 

F    8     53 

Fi6      o 

Fl2       20 

S    i       7 

31 

S6       8 

So       i 

F  10     32 

Fi6     18 

Fio     32 

S    3     33 

Retardation  of  Sunset  near  the  Winter  Solstice.  — About 
Christmas  time  in  our  latitudes  we  may  begin  to  look  for 
the  lengthening  of  the  day,  which-  betokens  the  return  of 
spring.  At  first  the  increase  is  very  slight,  perhaps  only 
two  or  three  minutes  in  the  course  of  a  week.  And  it 
is  commonly  observed  that  the  increase  takes  place  in  the 
afternoon  half  of  the  day ;  that  is,  the  sun  sets  later  and 
later  each  day,  although  its  time  of  rising  does  not  show 
much  change  until  the  middle  or  latter  part  of  January. 
The  reason  of  this  is  that  sunrise  and  sunset  are  calculated 
for  the  real  sun  ;  but  the  times  themselves  are  mean  times, 
that  is,  time  according  to  the  fictitious  sun.  The  real  sun 
TODD'S  ASTRON.  —  8 


The  Earth   Turns  on  its  Axis 


is  fast  about  five  minutes  in  the  middle  of  December,  so 
that  the  afternoon  is  ten  minutes  shorter  than  the  fore- 
noon. But  the  equation  of  time  is  diminishing  rapidly  ; 
that  is,  the  real  sun  is  moving  eastward  more  rapidly  than 
the  fictitious  sun,  and  will  soon  coincide  with  it,  making 
the  equation  of  time  zero.  On  account  of  this  eastward 
motion  of  the  real  sun,  more  rapidly  than  usual,  its  mean 

time  of  setting  is  re- 
tarded so  much  that  the 
effect  begins  to  be  ap- 
parent as  a  lengthening 
of  the  day,  even  before 
the  sun  reaches  the  sol- 
stice. After  the  solstice 
is  passed,  the  sun's  dec- 
lination is  less,  and  its 
longer  diurnal  arc  con- 
spires with  the  rapid 
eastward  movement  of 
the  real  sun  ;  so  that  by 
the  end  of  December 
both  causes  make  the 
sun  set  a  minute  later 
each  day.  For  a  similar 
reason,  operating  at  the 
summer  solstice,  the 
forenoon  half  of  the  day 
begins  to  shorten  as 
early  as  the  middle  of 


Antique  Form  of  Clepsydra 


June. 


Time  Keepers  of  the  Ancients.  —  It  is  not  known  that  the 
ancients  had  any  clocks  similar  to  ours ;  but  they  meas- 
ured the  lapse  of  time  by  clepsydras  and  sundials.  Fre- 
quently also  the  gnomon,  or  pointed  pillar,  was  used. 


To  Find  Trite  North  1 1 5 

A  clepsydra  is  a  mechanical  contrivance  for  measuring  and  indicating 
time  by  means  of  the  flow  of  water.  The  illustration  shows  a  common 
form.  Water  is  supplied  freely  to  the  conical  vessel,  an  overflow  main- 
taining always  a  given  level,  so  that  the  pressure  at  bottom  is  con- 
stant. Through  a  small  aperture  and  pipe,  the  water  drops  into  a 
larger  cylindrical  vessel  which  fills  very  slowly.  On  the  surface  of  the 
water  in  it  rests  a  float,  attached  to  which  is  an  upright  ratchet  rod. 
Working  into  the  teeth  of  this  are  the  teeth  of  a  cog  wheel,  and  on  the 
same  arbor  with  it  is  a  single  hand,  which  revolves  round  the  dial  and 
marks  the  progress  of  the  hours.  With  a  contrivance  of  this  sort,  time 
could  be  told  within  five  or  six  minutes.  The  day  of  the  ancients,  that 
is,  the  variable  interval  between  sunrise  and  sunset,  was  always  divided 
into  12  hours;  therefore  the  day  continually  differed  in  length.  By 
changing  the  aperture  at  bottom  of  the  conical  vessel,  the  clepsydra 
was  regulated  and  made  to  keep  pace  with  the  variable  hours. 

Sundial  Time.  —  The  time  indicated  by  a  sundial  is 
apparent  solar  time,  and  no  ordinary  clock  can  follow  it, 
except  by  accident.  Previously  to  the  nineteenth  century, 
however,  the  attempt  was  made  to  construct  clocks  with 
such  compensating  devices  that  they  would  gain  or  lose, 
as  referred  to  the  stars,  just  as  the  sun  does.  But  varia- 
tions in  the  sun's  apparent  motion  are  so  complex  that 
fine  machinery  necessary  to  follow  the  sun  with  precision 
could  scarcely  be  made,  even  at  the  present  day.  Certainly 
its  construction  was  impossible  a  century  ago. 

Early  in  the  igth  century  apparent-time  clocks  were  generally  aban- 
doned, although  in  Paris  they  were  in  use  as  late  as  1815.  Elaborate 
sundials  are  still  occasionally  met  with,  but  their  purpose  is  ornamental 
rather  than  useful.  In  a  form  of  sundial  easily  constructed,  a  wire  is 
adjusted  parallel  to  the  earth's  axis,  and  its  shadow  falling  upon  a 
divided  circular  arc  parallel  to  the  equator  tells  the  apparent  time. 

To  find  True  North  quite  Accurately.  —  As  a.  preliminary  to  the 
arrangements  for  setting  up  any  instrument  in  the  meridian,  or  mount- 
ing it,  as  the  technical  expression  is,  true  north  must  first  be  found  with 
some  accuracy.  Select  a  window7  with  a  northern  exposure,  and  a  view 
down  nearly  to  the  north  (sensible)  horizon.  From  the  top  casing  of 
the  window,  hang  a  long  plumb-line,  allowing  the  bob  to  swing  freely 
in  a  basin  of  water.  Secure  it  where  it  comes  to  rest,  stretching  the 
line  taut.  From  a  small  table  in  the  room  hang  another  plumb-line  in 
a  similar  manner,  using  fine,  light-colored  cord  or  cotton  for  the  lines. 


1 1 6  The  Earth    Turns  on  its  Axis 

These  arrangements  should  be  made  beforehand,  as  in  the  illustra- 
tion. The  problem  is  to  adjust  the  short  line  relatively  to  the  long 
one,  so  that  the  vertical  plane  passing  through  the  two  plumb-lines 


Finding  True  North  without  Clock  or  Telescope  (from  a  Photograph  by  Lovell) 

shall  pass  also  through  the  pole  star  when  crossing  the  meridian.  This 
vertical  plane  will  then  itself  be  the  meridian,  and  must  therefore 
intersect  the  horizon  in  the  true  north  and  south  points.  But  we  have 
seen  that  the  pole  star,  not  being  exactly  at  the  north  pole,  describes 
a  very  small  circle  of  the  celestial  sphere  once  every  24  sidereal  hours  ; 
therefore  it  must  cross  the  meridian  twice  during  that  period.  The 
intervals  between  these  crossings  will  be  nearly  12  ordinary  hours.  It 
is  not  at  all  necessary  to  know  the  exact  local  or  ordinary  time  when 


A  Rudimentary   Transit  Instrument       1 1 7 

the  pole  star  is  at  the  meridian;  but  Polaris  always  comes  into  this 
position  whenever  Mizar  (Zeta  Ursae  Majoris,  the  middle  star  in  the 
handle  of  the  Dipper)  is  also  on  the  meridian.  So  it  is  only  requisite 
to  watch  closely  for  the  time  when  the  long  plumb-line  passes  through 
both  these  stars ;  then,  placing  the  eye  near  the  floor,  to  move  the 
table  carefully  until  the  short  plumb-line  hangs  in  the  same  plane  with 
the  long  line  and  both  stars.  Be  sure  that  the  short  plumb-line  hangs 
perfectly  free  and  still.  A  candle  placed  behind  the  observer's  head 
will  show  both  lines,  and  at  the  same  time  not  obscure  the  stars.  Then 
by  two  permanent  marks  in  the  plane  of  the  plumb-lines,  establish  the 
meridian  for  convenient  use.  In  line  with  Mizar  and  Polaris,  and 
about  as  far  on  the  opposite  side  of  the  pole,  there  chances  to  be 
another  star,  Delta  Cassiopeiae,  which,  therefore,  can  be  used  in  the 
same  way  as  Mizar  itself.  Through  nearly  the  entire  year,  either  one 
or  the  other  of  these  stars  is  available  for  finding  true  north,  without 
any  reference  whatever  to  the  clock. 

Times  when  Mizar  and  Delta  Cassiopeise  are  on  the  lower  Merid- 
ian. —  Begin  watching  before  the  lower  star  comes  to  the  meridian. 
It  will  then  appear  to  the  left  of  the  long  plumb-line  hanging  through 
Polaris.  Here  is  a  table  showing  when  to  begin  to  watch  :  — 

FOR  8  CASSIOPEIA  FOR  MIZAR 

Dec.  20  7  A.M.  July    20  5  A.M. 

Jan.  20  5  A.M.  Aug.  20  3  A.M. 

Feb.  20  3  A.M.  Sept.  20  i  A.M. 

Mar.  20  i  A.M.  Oct.    20  11  P.M. 

Apr.  20  ii  P.M.  Nov.  20  9  P.M. 

May  20  9  P.M.  Dec.  20  7  P.M. 

June  20  7  P.M.  Jan.    20  5  P.M. 

Both  stars  come  about  four  minutes  earlier  every  day,  just  as  the 
south  star  did.  During  a  part  of  June  and  July  this  method  cannot  be 
used,  because  it  is  strong  twilight  or  daylight  when  Mizar  and  Delta 
Cassiopeiae  are  crossing  the  meridian.  If  repeated  on  a  subsequent 
night,  this  method  of  establishing  the  local  meridian  will  be  found 
sufficiently  accurate  for  mounting  any  astronomical  instrument.  Its 
adjusting  screws  will  then  bring  it  into  closer  range,  when  the  telescope 
can  be  brought  into  service  to  show  the  amount  of  deviation.  If  no 
telescope  is  available,  a  transit  instrument  may  be  made  of  a  few  com- 
mon materials,  and  the  local  time  found  by  it  approximately. 

A  Rudimentary  Transit  Instrument.  —  The  methods  astronomers 
use  in  finding  accurate  time  will  be  sketched  in  outline  in  Chapter  ix. 
We  here  describe  a  method  of  getting  the  time  within  a  few  seconds  by 


n8 


The  Earth   Turns  on  its  Axis 


an  observation  of  the  sun.  In  the  open  air,  or  in  a  south  window 
with  a  clear  meridian  from  the  south  nearly  up  to  the  zenith,  hang 
two  fine  plumb-lines  accurately  in  the  meridian  by  the  method  just 
given.  In  line  with  them,  firmly  attach  a  strong  box  (about  18  inches 
square)  to  the  window  casing,  as  shown  in  the  illustration ;  or  better, 
to  the  east  or  west  side  of  a  building.  By  sighting  along  the  plumb- 
lines,  run  a  pencil  mark  round  the  outside  of  the  box,  to  indicate  the 


Observing  the  Time  of  Apparent  Noon  with  the  Box-transit 

meridian  roughly.  Bore  two  ^-inch  holes  in  this  mark,  at  points  A  and 
B.  Also  bore  a  third  in  the  same  plane  near  the  middle  of  the  upper 
face  of  the  box.  Over  this  lay  a  strip  of  sheet  lead  or  tin,  with  a  smooth 
pin  hole  through  it,  tacking  it  carefully  so  that  the  pin  hole  shall  be  in  the 
plane  of  both  plumb-lines.  By  sighting  past  these  lines  and  through 
the  holes  A  and  B,  draw  a  fine  straight  pencil  mark  on  the  inside  of  the 
lower  face  of  the  box,  as  shown,  exactly  in  the  plane  of  the  plumb-lines. 
If  the  box  is  exposed  to  the  weather,  this  transit  line  may  be  scratched 
on  a  strip  of  tin,  which  may  then  be  tacked  in  position  by  sighting 
through  the  holes  A  and  B. 

If  star  transits  are  to  be  observed  in  the  open,  a  different  arrange- 
ment of  the  meridian  plane  is  necessary.  Connect  together  the  two 
ends  of  a  fine  brass  or  copper  wire  about  20  feet  long ;  pass  it  over  two 
ooints  in  the  meridian  about  6  feet  apart  (north  one  perhaps  two  feet 


How  Observatory   Time  is  Found          119 

above  the  south  one)  ;  hook  a  heavy  weight  on  the  wire  underneath, 
and  when  it  stops  swinging,  fasten  the  double  wire  firmly.  Bright 
stars  at  all  meridian  altitudes  can  be  observed  to  cross  this  'triangle 
transit,1  with  an  error  of  only  a  few  seconds.  Comparison  with  a  list 
of  their  right  ascensions  will  then  give  the  sidereal  time. 

Observing  the  Sun's  Transit. — Just  before  noon,  a  small  round  spot 
of  light  will  be  seen  to  the  west  of  the  inside  mark.  It  is  an  image  of 
the  sun  itself,  about  -^  inch  in  diameter ;  and  it  will  be  pretty  sharply 
defined  if  the  pin  hole  is  smooth  and  round.  The  extreme  positions  of 
the  image  at  the  solstices  are  shown  in  the  illustration.  Watch  the 
image  as  it  slowly  creeps  toward  the  transit  line ;  observe  the  time 
with  a  watch  when  its  edge  first  touches  the  line :  there  will  be  an  un- 
certainty of  perhaps  five  seconds.  Rather  more  than  a  minute  later  the 
image  will  be  bisected  by  the  line  ;  observe  this  time  also,  likewise  ob- 
serve the  time  when  the  following  edge  or  limb  of  the  sun  becomes  tan- 
gent to  the  line.  Take  the  average  of  the  three ;  add  or  subtract  the 
equation  of  time,  as  given  in  the  table  on.  page  113.  The  result  will  be 
local  mean  time,  within  a  small  fraction  of  a  minute,  provided  the 
plumb-lines  have  been  delicately  adjusted  in  the  meridian,  and  the  geo- 
metric constructions  of  the  transit  box  have  been  carefully  made.  A 
farther  and  constant  correction  will  be  required  when  the  watch  keeps 
standard  time :  if  the  place  of  observation  is  west  of  the  standard  me- 
ridian, add  the  amount  of  this  difference  of  longitude  in  time ;  if  to  the 
east  of  it,  subtract  this  difference. 

Calculating  the  Sun's  Transit.  —  On  the  5th  of  February,  1897,  at 
Amherst,  Massachusetts  (2°  28'  50"  =  9  m.  55  s.  east  of  the  standard 
meridian),  the  following  times  of  transit  were  observed  with  the  watch  :  — 

h.  m.  s. 

First  limb  of  O  tangent,          12  24  8 

Sun  bisected,                           12  25  25 

Second  limb  of  O  tangent,     12  26  33 

Mean,  12    25     22=watch  time  of  apparent  noon. 

Because  sun  is  slow,  subtract        14     i6=equation  of  time. 

Difference,  12     n       6= watch  time  of  Amherst  mean  noon. 

Subtract  for  longitude,  9    55= east  of  Eastern  Standard  meridian. 

Difference,  12      i     11= watch  time  of  noon  at  standard  meridian. 

12      o      o 

Difference,  i     11= watch  fast  of  standard  time. 

How  Observatory  Time  is  found.  —  Recall  the  method 
of  counting  right  ascensions  of   the    heavenly  bodies  — 
eastward  along  the  celestial  equator  from  the  vernal  equi- 
nox to  the  hour  circle  of  the  body,  counting  from  o  h.  round 


I2O  The  Earth   Turns  on  its  Axis 

to  24.h.  Sidereal  time,  as  has  just  been  shown,  elapses  in 
precisely  the  same  way —  from  o  h.  o  m.  o  s.  when  the  ver- 
nal equinox  is  crossing  the  meridian,  round  to  24  h.  6  m.  o  s., 
when  it  is  next  on  the  meridian.  Clearly,  then,  any  star  is 
on  the  meridian  when  the  sidereal  time  is  equal  to  its  right 
ascension.  But  the  right  ascensions  of  all  the  brighter  stars 
have  been  determined  by  the  labor  of  astronomers  in  the 
past,  and  are  set  down  in  the  Ephemeris  and  in  star  cata- 
logues. Also  the  same  is  given  for  sun,  moon,  and  planets. 
Therefore,  in  practice,  it  is  the  converse  of  this  relation 
which  concerns  us  in  the  problem  of  rinding  the  time  by 
observing  the  transit  of  a  heavenly  body.  Simply  observe 
the  time  of  its  transit  by  the  sidereal  clock :  if  this  time  is 
the  same  as  the  body's  right  ascension,  the  clock  has  no 
error.  If,  as  nearly  always  happens,  the  time  of  transit 
differs  from  the  right  ascension,  this  difference  is  the  cor- 
rection of  the  clock ;  that  is,  the  amount  by  which  it  is  fast 
or  slow.  Once  the  correction  of  the  sidereal  clock  is 
found,  the  eiror  of  any  other  timepiece  is  ascertained 
from  comparison  with  it.  In  observatories  the  mean  solar 
time  is  rarely  found  by  direct  observation ;  but  it  is  cus- 
tomary to  compare  the  mean-time  clock  with  the  sidereal 
clock,  and  then  calculate  the  corresponding  mean  time  by 
using  the  'sidereal  time  of  mean  noon.' 

Relation  between  Sidereal  and  Solar  Time.  —  This  rela- 
tion has  been  found  by  astronomers  with  the  utmost  pre- 
cision, and  the  quantities  concerned  in  it  are  constantly  used 
by  them  in  ascertaining  accurate  time.  The  true  relation 
is  this :  First,  find  how  far  the  fictitious  sun  travels  east- 
ward in  one  day.  As  it  goes  all  the  way  round  the  celes- 
tial equator  (360°)  in  one  year,  or  365^  days,  evidently  in 
one  day  it  travels  nearly  a  whole  degree  (59'  8". 3 3,  ac- 
curately). This  angle,  as  we  shall  see  in  the  next  chapter, 
is  nearly  twice  the  apparent  breadth  of  the  sun.  Now  dur- 


The  Sidereal  Time  of  Mean  Noon         121 


ing  a  sidereal  day  an  arc  of  360°, 
or  the  entire  equator  of  the  heavens, 
passes  the  meridian  of  any  given 
place.  Therefore  in  a  mean  solar 
day,  an  arc  of  the  equator  equal  to 
nearly  361°  (accurately  360°  59'  8^.33) 
must  pass  the  same  meridian.  From 
this  relation  we  can  calculate  by 
simple  proportion  that 

24  mean  solar  hours  ?o 

=  24  h.    4m.  sidereal  time  & 

(accurately,  24  h.  3  m.  56.555  s.),  § 

and  24  sidereal  hours  2, 
=  23  h.  56  m.  mean  solar  time 
(accurately,  23  h.  56  m.  4.091  s.). 

SL 

But  we  saw  that  the  sidereal  day  of  $ 
24  sidereal  hours  is  the  true  period  | 
of  rotation  on  its  axis.  One  must,  ^ 
therefore,  guard  against  saying  that  1 
the  period  of  the  earth's  rotation  on  f 
its  axis  is  24  hours,  unless  specifying  "g. 
that  sidereal  hours  are  meant.  By  j 
the  term  hour,  as  ordinarily  used  jj, 
without  qualification,  the  mean  solar  I 
hour  is  understood.  So  that  the  $ 
true  period  in  which  the  earth  turns  *"* 
once  on  its  axis  is,  not  24  hours,  but 
23  h.  56m.  4.095. 

The  Sidereal  Time  of  Mean  Noon. 
—  At  every  working  observatory  are 
two  clocks,  the  one  keeping  sidereal 
time,  the  other  mean  solar  time.  Let 
us  imagine  both  regulated  to  run 
perfectly.  About  the  2Oth  March, 
at  mean  noon,  when  the  fictitious 


SEPTEMBER 


0  NOVEMBER 


*» — i-4C    •— ^J 


)^TRCH 


122 


The  Earth  Turns  on  its  Axis 


sun  crosses  the  equinoctial  colure,  start  both  clocks  at  o  h., 
o  minutes,  o  seconds,  indicated  by  both  dials.  At  the 
next  mean  noon,  the  mean-time  clock  will  have  come 
round  to  o  h.  o  m.  o  s.  again,  marking  the  beginning  of 
a  new  astronomical  day;  but  the  sidereal  clock  will 
indicate  at  the  same  instant  oh.  3m.  56.55  s.,  because  it 
has  gained  this  difference  during  the  24  hours.  At  mean 
noon  the  next  following  day  the  sidereal  clock  will  indi- 
cate oh.  /m.  53. 1 1  s. ;  and  so  on,  perpetually  gaining  nearly 
4m.  every  day.  The  figure  just  given  makes  this  relation 
plain  for  a  complete  cycle  of  a  year.  The  time,  then, 

TABLE  FOR  FINDING  THE  SIDEREAL  TIME  OF  MEAN  NOON 


To  THE  MEAN 

TIME 

ADD  THE  FOLLOW- 
ING QUANTITY 

To  THE  MEAN 

TIME 

ADD  THE  FOLLOW- 
ING QUANTITY 

h. 

m. 

h. 

m. 

January    .     . 

I 

18 

45 

July  .     .     . 

I 

6 

40 

15 

19 

40 

15 

7 

35 

February  .     . 

I 

20 

45 

August  .     . 

I 

8 

40 

15 

21 

40 

15 

9 

40 

March  .     .     . 

I 

22 

40 

September  . 

I 

10 

45 

15 

23 

35 

15 

ii 

40 

April    .     .     . 

I 

0 

40 

October 

I 

12 

45 

15 

I 

35 

15 

13 

40 

May     .     .     . 

I 

2 

40 

November  . 

I 

14 

45 

15 

3 

35 

15 

15 

40 

June     .     .     . 

I 

4 

40 

December  . 

I 

16 

45 

15 

5 

40 

15 

17 

40 

July     .,    .     . 

I 

6 

40 

January  .     . 

I 

18 

45 

shown  (at  each  mean  noon)  by  a  sidereal  clock  perfectly 
adjusted,  is  called  the  '  sidereal  time  of  mean  noon.'  *    But 

*  An  approximate  value  is  easily  found  by  the  above  table :  if  the  given 
day  is  not  the  1st  or  the  I5th,  find  the  proper  additive  quantity  by  applying  4 
minutes  for  each  day  before  or  after  the  nearest  day  given  in  the  table. 


Ascertaining  Longitude  123 

as  no  clock  can  be  made  to  carry  on  the  time  with  absolute 
accuracy,  these  times  are,  in  practice,  not  taken  from  a 
clock,  but  they  are  calculated  and  published  in  the  Ephem- 
eris,  a  set  of  astronomical  tables  issued  by  the  Govern- 
ment two  or  three  years  in  advance.  As  the  sidereal  times 
of  all  the  mean  noons  through  the  year  are  absolutely 
accurate  for  all  places  on  the  prime  meridian,  they  can  be 
adapted  to  any  place  by  simply  applying  a  constant  cor- 
rection dependent  on  its  longitude.  Clearly  it  is  necessary 
to  know  the  sidereal  time  of  mean  noon,  if  we  desire  to 
compare  mean  time  with  sidereal  time  at  any  instant ;  and 
this  calculation  of  one  kind  of  time  from  the  other  is  the 
most  frequent  problem  of  the  practical  astronomer.  It  can 
be  made  in  a  minute  or  two,  and  is  accurate  to  the  T^  part 
of  a  second. 

Ascertaining  Longitude.  —  Longitude  is  angular  distance 
measured  on  the  earth's  equator  from  a  prime  meridian  to 
the  meridian  of  the  place.  In  England  the  prime  meridian 
passes  through  the  Royal  Observatory  at  Greenwich,  the 
prime  meridian  of  France  passes  through  the  Paris  Ob- 
servatory, and  the  prime  meridian  of  the  United  States 
passes  through  the  Observatory  at  Washington.  Longitude 
is  given  in  either  arc  or  time.  As  the  earth  by  turning 
round  uniformly  on  its  axis  affords  our  measure  of  time, 
the  meridians  of  the  globe  must  pass  uniformly  underneath 
the  stars ;  so  that  finding  the  longitude  of  a  place  is  the 
same  thing  as  finding  how  much  its  local  time  is  fast  or 
slow  of  the  local  time  of  the  prime  meridian. 

Transit  instruments  are  mounted  and  carefully  adjusted  at  the  two 
places  whose  difference  of  longitude  is  sought.  By  a  series  of  observa- 
tions (usually  of  transits  of  stars),  local  sidereal  time  at  each  place 
is  ascertained.  Then  time  at  both  stations  is  automatically  com- 
pared by  means  of  the  electric  telegraph,  and  the  difference  of  their 
times  is  the  difference  of  their  longitudes,  expressed  in  time.  The  place 
at  which  the  time  is  faster  is  the  farther  east.  If  there  is  no  telegraph 


124  The  Earth   Turns  on  its  Axis 

line  or  cable  connecting  the  two  stations,  indirect  and  much  less  accu- 
rate methods  of  comparing  their  local  times  must  be  resorted  to.  So 
precise  is  the  telegraphic  method  that  the  distance  of  Washington  from 
Greenwich  is  known  with  an  error  probably  not  exceeding  300  feet  on 
the  surface  of  the  globe ;  and  where  only  land  lines  are  employed,  the 
distance  of  one  place  from  another  may  be  found  even  more  accurately. 
Usually  the  time  will  be  determined  and  signals  exchanged  on  a  series 
of  six  or  eight  nights  ;  and  the  entire  operation  of  finding  the  longitude 
is  called  a  longitude  campaign. 

Standard  Time.  —  Formerly,  in  traveling  even  a  few 
miles,  one  was  subjected  to  the  annoyance  of  changing 
one's  watch  to  the  local  time  of  the  place  visited.  The 
actual  difference  between  Boston  and  New  York  is  12 
minutes  —  between  New  York  and  Washington  12  min- 
utes ;  and  until  within  a  few  years  each  place  kept  only  its 
own  local  time.  But  it  was  decided  to  establish  a  standard 
of  time  by  which  railroad  trains  should  run  and  all  ordinary 
affairs  be  regulated;  and  in  November  of  1883  this  plan 
was  adopted  by  the  country  at  large,  and  time  signals  from 
Washington  are  now  distributed  throughout  the  United 
States  every  day  at  noon.  The  whole  country  is  divided 
into  four  sections,  or  meridian  belts,  approximately  15 
degrees  of  longitude  in  width,  so  that  each  varies  from 
those  adjacent  to  it  by  exactly  an  hour.  The  time  in  the 
whole  *  Eastern  '  section  is  that  of  the  /5th  meridian  from 
Greenwich,  making  it  five  hours  slower  than  Greenwich 
time.  This  standard  meridian  coincides  almost  exactly 
with  the  local  time  of  Utica  and  Philadelphia,  and  extends 
to  Buffalo.  Beyond  that,  watches  are  set  one  hour  earlier, 
and  the  'Central'  section  begins,  just  six  hours  slower 
than  Greenwich  time,  employing  QOth  meridian  time,  which 
is  almost  exactly  that  of  actual  time  at  Saint  Louis. 
This  division  extends  to  the  center  of  Dakota,  and  in- 
cludes Texas.  '  Mountain'  or  iO5th  meridian  time  is  yet 
another  hour  earlier,  seven  hours  slower  than  Greenwich, 


Standard  Time  in  Foreign  Countries       125 

and  is  nearly  Denver  local  time.  It  extends  to  Ogden, 
Utah;  and  the  'Pacific'  section,  using  i2Oth  meridian 
time,  is  eight  hours  behind  Greenwich,  and  ten  minutes 
faster  than  local  time  at  San  Francisco. 

This  simplifies  all  horological  matters  greatly,  especially  the  run- 
ning of  trains  on  the  great  railroads.  While  theoietically  equal,  these 
divisions  are  by  no  means  so  in  reality,  because  variation  is  made  from 
the  straight  line,  in  order  to  run  each  railroad  system  through  on  the 
same  time,  or  make  the  change  at  great  junctions.  The  cittes  just  at 
the  changing  points  may  use  either,  and  they  make  their  own  choice, 
Buffalo,  for  instance,  choosing  Eastern  time,  though  Central  would 
have  been  equally  appropriate  ;  and  Ogden  choosing  Mountain  instead 
of  Pacific.  Wherever  standard  time  is  kept,  the  minute  and  second 
hands  of  all  timepieces  are  the  same.  Only  the  hours  differ.  In 
journeying  from  one  meridian  belt  into  the  next,  it  is  only  necessary  to 
change  one's  watch  by  an  entire  hour,  setting  it  ahead  an  hour  if 
traveling  eastward,  and  turning  it  back  an  hour  when  journeying  west. 
In  this  country,  accurate  time  is  distributed  by  time  balls,  dropped 
at  Boston,  New  York,  Washington,  and  elsewhere,  and  by  self-winding 
clocks  controlled  through  the  circuits  of  the  Western  Union  Telegraph 
Company.  The  New  York  time  ball  is  illustrated  on  page  9. 

Standard  Time  in  Foreign  Countries.  —  Within  very  re- 
cent years,  the  adoption  of  standard  time  has  become 
nearly  universal  among  the  leading  governments  of  the 
world.  Almost  without  exception,  the  standard  merid- 
ians adopted  are  a  whole  number  of  hours  from  the 
prime  meridian  of  Greenwich,  and  local  time  in  different 
parts  of  the  world,  corresponding  to  Greenwich  noon,  is 
shown  in  the  Mercator  map  (page  127).  In  a  few  in- 
stances, where  a  country  lies  almost  wholly  between  two 
such  meridians,  its  accepted  standard  of  time  is  referred 
to  the  half-hour  meridian  between  the  two.  In  some 
European  cities,  particularly  London  and  Paris,  accurate 
time  is  distributed  automatically  from  a  standard  clock  at 
a  central  station,  or  observatory.  The  more  important 
foreign  countries  where  standard  time  is  used,  with  their 
adopted  standards,  are  as  follows  :  — 


126  The  Earth    Turns  on  its  Axis 

STANDARD  TIME  IN  FOREIGN  COUNTRIES 


COUNTRY 

STANDARD 
MERIDIAN 
EAST  OF 
GREENWICH 

TIME 
FAST  OF 
GREENWICH 

COUNTRY 

STANDARD 
MERIDIAN 
EAST  OF 
GREENWICH 

TIME 
FAST  OF 
GREENWICH 

h.  m.    s. 

h.      m. 

Great  Britain 

0°    0' 

000 

Cape  Colony  . 

22°    30' 

I      30 

France 

2     20 

0921 

Natal    .     .     . 

30       o 

2       0 

Germany  .     . 

15      o 

I    O     O 

West       Aus- 

Italy   .     .     . 

15      o 

I    O     O 

tralia 

120         0 

8      o 

Austria     .     . 

15      o 

I    0     0 

Japan   .     .     . 

135          0 

9     ° 

Denmark  .     . 

15      o 

0     0 

S.  Australia  . 

135          ° 

9     o 

Norway    . 

15      o 

0     0 

Victoria    .     . 

150      o 

10        0 

Sweden     . 

15      o 

0     0 

Queensland    . 

150      o 

10        0 

Belgium    . 

15      o 

o    o 

Tasmania  . 

150      o 

IO        O 

Holland    .     . 

15      o 

o    o 

New  Zealand  . 

172   30 

II    30 

Travelers  in  these  countries,  therefore,  have  only  to  set  their  watches 
according  to  these  differences  of  time.  In  general,  it  is  evident  that 
only  the  hour  hand  needs  changing,  the  minutes  and  seconds  remain- 
ing the  same  as  in  England  or  America.  The  second  and  minute 
hands  of  all  clocks  and  watches  keeping  exact  standard  time  in  the 
United  States,  Japan,  Australia,  and  nearly  the  whole  of  Europe  read 
the  same :  their  hour  hands  alone  differ. 

Uniformity  of  the  Earth's  Rotation.  —  It  is  now  clear 
that  the  turning  of  the  earth  on  its  axis  is  of  very  great 
service,  not  only  to  the  astronomer  in  making  his  investi- 
gations, but  to  mankind  in  general,  as  affording  a  very 
convenient  means  of  measuring  time.  Everything  is  based 
on  the  absolute  uniformity  of  this  rotation.  Reliance  is  — 
indeed,  must  be — implicit.  Yet  it  is  possible  to  test  this 
important  element  by  comparing  it  with  known  move- 
ments of  other  bodies  in  the  sky,  particularly  the  moon, 
the  earth,  and  the  planet  Mercury  round  the  sun.  The 
deviations,  if  any,  are  nearly  inappreciable ;  and  the  slight 
slackening  of  its  rotation  at  one  period  seems  to  be  coun- 


"7 


128 


The  Earth    Turns  on  its  Axis 


terbalanced  by  an  equal  acceleration  at  another.  So  that 
if  irregularities  actually  do  exist,  they  probably  cancel  each 
other  in  the  long  run,  and  leave  the  day  invariable  in 
length.  Uniformity  of  the  earth's  rotation  has  been  criti- 
cally investigated 
by  Newcomb,  and 
no  change  in 
the  length  of  the 
day  as  great  as 
ToW  of  a  second 
in  a  thousand  years 
could  escape  de- 
tection. 

Precession  of  the 
Equinoxes ,  —  The 
equinoxes  have  a 
slow  motion,  partly 
produced  by  the 
earth's  turning  on 
its  axis.  The  eclip- 
fc  tic  remains  invari- 
able in  position, 
and  equator  and 
ecliptic  are  always 
inclined  to  each 
other  at  practically 
the  same  angle ;  but  this  motion  of  the  equinoxes  is  a  glid- 
ing of  equator  round  ecliptic,  and  is  called  precession.  The 
equinoxes  travel  westward  about  50^'  annually ;  so  that 
in  rather  less  than  13,000  years,  the  vernal  equinox  will 
have  slipped  round  to  the  position  formerly  occupied  by 
the  autumnal  equinox.  In  25,900  years  precession  com- 
pletes an  entire  cycle,  both  equinoxes  returning  to  their 
position  at  the  beginning  of  it. 


A  Model  to  illustrate  Precession 


Effects  of  Precession  129 

Precession  is  so  important  in  astronomy  that  the  phenomenon 
should  be  perfectly  understood.  Over  a  tub  nearly  filled  with  water, 
suspend  a  barrel  hoop  by  three  cords,  two  of  which,  equal  in  length, 
are  attached  to  the  hoop  at  the  extremities  of  a  diameter.  The  third 
cord,  a  few  inches  shorter  than  the  other  two,  is  tied  to  the  hoop  mid- 
way between  them.  Fasten  three  weights  of  about  one  pound  each  at 
the  same  points.  Gather  the  three  cords  together  into  one,  at  a  few 
feet  above  the  hoop,  and  tie  them  to  a  right-hand-twisted  cord  a  few 
feet  long.  To  represent  the  earth,  with  axis  perpendicular  to  the  hoop, 
secure  any  common  spherical  object  in  the  center  of  the  hoop,  by  a 
crosspiece  nailed  to  hoop  as  indicated.  Suspend  the  whole  by  the 
twisted  cord  as  shown  in  the  picture,  lowering  it  until  the  hoop  is  im- 
mersed to  the  knots  of  the  two  short  cords.  These  represent  the 
equinoxes,  the  hoop  itself  the  celestial  equator,  and  the  surface  of  water 
in  the  tub  stands  for  plane  of  ecliptic.  Adjust  the  shorter  cord  so  that 
the  hoop  shall  be  tilted  to  the  water  about  23 1°.  Now  release  the  hoop, 
and  it  will  twirl  round  clockwise  ;  the  motion  of  the  two  opposite  knots 
will  correspond  to  precession  of  the  equinoxes,  and  represent  the  long 
period  of  precession,  25,900  years  in  duration.  This  motion  round  the 
signs  of  the  zodiac  (in  the  direction  Aries,  Pisces,  Aquarius),  is  repre- 
sented by  the  arrow  in  the  illustration  on  page  65.  Pole  of  ecliptic  is 
£",  and  round  it  as  a  center  moves  P,  the  earth's  pole,  in  a  small  circle, 
PpS V,  47°  in  diameter. 

Effects  of  Precession.  —  On  account  of  precession,  right 
ascensions  and  decimations  of  stars  (being  referred  to  the 
equator  as  a  fundamental  plane)  are  continually  changing. 
Precession  of 
the  equinoxes 
was  first  found 
out  by  Hippar- 
chus  (B.C.  150). 
About  B.C.  2200, 
the  vernal  equi- 
nox was  near 

JL.         •%«••,  Vernal  Equinox  in  Taurus  (B  C.  2200) 

the   Pleiades  as 

in  the  adjacent  figure.     Since  that  time  it  has  traveled 
back,  or  westward,  about  60°,  through  Aries,  until  now  it  is 
in  the  western  part  of  Pisces,  as  on  the  following  page.    So 
TODD'S  ASTRON.  —  9 


130  The  Earth    Turns  on  its  Axis 

the  signs  of  the  zodiac  do  not  now  correspond  with  con- 
stellations which  bear  the  same  names,  as  they  did  in  the 
time  of  Hipparchus ;  and  the  two  systems  are  becoming 
more  and  more  separated  as  time  elapses.  Because  the 
direction  of  earth's  axis  in  space  is  changing,  the  north 

celestial  pole  is  slowly 
moving  among  the 
stars,  in  a  small  circle 
whose  center  is  the 
north  pole  of  the  eclip- 
tic; and  it  will  complete 
its  circle  in  the  period  of 

Vernal  Equinox  now  in  Pisces  prCCCSSion  itself.      That 

important  star  Polaris,  our  present  north  star  because  now 
so  near  the  intersection  of  earth's  axis  prolonged  north- 
ward to  the  sky,  has  not  always  been  the  pole  star  in  the 
past,  nor  will  it  always  be  in  the  future.  If  circumpolar 
stars  were  photographed  in  trails,  as  on  page  33,  at  inter- 
vals of  a  few  hundred  years,  the  curvature  of  arcs  traversed 
by  a  given  star  would  change  from  time  to  time.  About 
200  years  hence,  the  true  north  pole  will  be  slightly 
nearer  Polaris  than  it  now  is,  and  afterward  the  pole  will 
retreat  from  it.  About  B.C.  3000,  Alpha  Draconis  was  the 
pole  star;  and  12,000  years  hence,  Vega  (Alpha  Lyrae) 
will  enjoy  that  distinction.  Regarding  positions  of  stars 
as  referred  to  the  ecliptic  system,  their  latitudes  cannot 
change,  because  ecliptic  itself  is  fixed.  But  longitudes  of 
stars  must  change,  much  as  right  ascensions  do,  because 
counted  from  the  moving  vernal  equinox.  Besides  rotation 
about  its  axis,  the  earth  has  another  motion  of  prime 
importance,  which  we  shall  now  discuss. 


CHAPTER  VII 

THE  EARTH  REVOLVES  ROUND  THE  SUN 

HITHERTO  explanation  has  been  given  only  of  that 
apparent  motion  of  the  heavenly  bodies  which  is 
common  to  all  —  a  rising  in  the  east,  crossing  the 
meridian,  and  setting  in  the  west.  Although  this  motion 
was  regarded  as  real  in  the  ancient  systems  of  astronomy, 
we  have  seen  that  it  is  satisfactorily  explained  as  a  purely 
apparent  motion,  due  to  the  simple  turning  round  of  the 
earth  on  its  axis  once  each  day.  Now  we  shall  consider 
an  entirely  different  class  of  celestial  motions ;  we  know 
that  they  take  place  because  our  observations  show  that 
none  of  the  bodies  which  are  tributary  to  the  sun  are 
stationary  in  the  sky.  This  point  will  be  fully  dwelt  upon 
in  a  subsequent  chapter  on  the  planets.  On  the  contrary, 
all  seem  to  be  in  motion  among  the  stars ;  at  one  time  for- 
ward or  eastward,  and  at  another  backward  or  toward  the 
west.  All  through  the  period  of  the  infancy  of  astronomy, 
a  fundamental  mistake  was  made  ;  too  great  importance 
was  attached  to  the  earth,  because  men  dwell  upon  it,  and 
it  seemed  natural  to  regard  it  as  the  center  about  which 
the  universe  wheeled.  Centuries  of  investigation  were 
required  to  correct  this  blunder;  and  true  relations  of 
the  celestial  mechanism  could  be  understood  only  when 
real  motions  had  been  thought  out  and  put  in  place  oi 
apparent  ones.  The  earth  was  then  forced  to  shrink  intc 
its  proper  and  insignificant  role,  as  a  planet  of  only  modest 


132        The  Earth  Revolves  Round  the  Sun 

proportions,  itself  obedient  in  motion  to  the  overpowering 
attraction  of  the  sun. 

The  Sun's  Apparent  Annual  Motion.  —  First,  let  us  again 
observe  the  sun's  seeming  motion  toward  the  east.  Soon 
after  dark,  the  first  clear  night,  observe  what  stars  are  due 
south  and  well  up  on  the  meridian.  A  week  later,  but  at 
the  same  time  of  the  evening,  look  for  the  same  stars  ; 
they  will  be  found  several  degrees  west  of  the  meridian. 
Why  the  change  ?  These  stars,  and  all  the  others  with 
them,  seern  to  have  moved  westward  toward  the  sun ;  or 
what  is  the  same  thing,  the  sun  must  have  moved  eastward 
toward  these  stars.  But  while  this  appears  to  be  a  motion 
of  the  sun,  we  shall  soon  see  that  it  is  really  a  motion  of 
the  earth  round  the  sun.  If  our  globe  had  no  atmosphere, 
the  stars  would  be  visible  in  the  daytime,  even  close  be- 
side the  sun ;  and  it  would  be  possible,  directly  and  with- 
out any  instruments,  to  see  him  approach  and  pass  by 
certain  stars  near  his  path  from  day  to  day.  A  few  obser- 
vations would  show  that  the  sun  seems  to  move  eastward 
about  twice  his  own  breadth,  that  is  i°,  every  day.  His 
path  among  the  stars  would  be  found  to  be  practically  the 
same  from  year  to  year.  This  annual  path  of  the  sun 
among  the  stars  is  called  the  ecliptic,  and  invariability 
of  position  has  led  to  its  adoption  by  astronomers  from 
the  earliest  times,  as  a  plane  of  reference.  Its  utility  as 
such  has  already  been  considered  in  Chapters  n  and  in ;  it 
is  the  fundamental  plane  of  the  ecliptic  system. 

Sun's  Apparent   Motion   really   the   Earth's   Motion.  - 
What  causes  that  apparent  motion  of  the  sun  just  described  ? 

Select  a  room  as  large  as  possible  in  which  there  is  a  tall  lamp. 
Place  this  in  the  center  of  the  room,  and  walk  around  it  counter-clock- 
wise, facing  the  lamp  all  the  time ;  notice  how  it  seems  to  move  round 
among  and  pass  by  the  objects  on  the  wall.  It  appears  to  travel  with 
the  same  angular  speed  that  you  do,  and  in  the  same  direction.  Now 
imagine  yourself  the  earth,  the  lamp  to  be  the  sun,  and  the  objects  on 


Earth's  Orbit  the  Ecliptic  Plane  133 

the  wall  the  fixed  stars.  The  horizontal  plane  through  the  lamp  and 
the  eye  will  represent  the  ecliptic;  one  complete  journey  round  the 
lamp  will  correspond  to  a  year. 

A  simple  experiment  of  this  character  will  convey  a 
clear  idea  of  the  true  explanation  of  the  sun's  apparent 
motion :  that  great  luminary  is  himself  stationary  at  the 
center  of  a  family  or  system  of  planets,  of  which  our  earth 
is  merely  one ;  and  our  globe  by  traveling  round  the  sun 
once  each  year  causes  him  to  appear  to  move.  If,  however, 
it  is  not  clear  how  the  earth's  motion  is  the  true  cause  of 
the  sun's  seeming  to  describe  his  annual  arc  round  the 
ecliptic,  put  yourself  in  place  of  the  lamp  and  have  some 
one  carry  the  lamp  round  you,  counter-clockwise.  Mean- 
while keep  your  eye  constantly  upon  the  lamp,  and  observe 
that  it  seems  to  move  round  on  the  wall  in  just  the  same 
direction  and  at  the  same  speed  as  when  the  lamp  was  sta- 
tionary and  you  walked  around  it. 

Earth's  Orbit  the  Ecliptic  Plane.  — The  real  path  which 
one  body  describes  round  another  in  space  is  called  its 
orbit.  The  path  our  globe  travels  round  the  sun  each  year 
is  called  the  earth's  orbit.  We  cannot  see  the  stars  close 
to  the  sun,  nor  observe  his  position  among  them  each  day ; 
but  practically  the  same  thing  is  done  by  means  of  instru- 
ments in  government  observatories.  While  these  observa- 
tions of  the  sun's  position  are  going  on  from  the  earth, 
imagine  a  similar  observatory  on  the  sun,  at  which  the 
earth's  positions  among  the  stars  are  recorded  at  the  same 
times.  Every  earth  observation  of  the  sun  will  differ  from 
its  corresponding  sun  observation  of  the  earth  by  exactly 
1 80°.  But  the  earth  observations  of  the  sun  are  all  in- 
cluded in  that  great  circle  of  the  sky  called  the  ecliptic, 
therefore  all  the  sun-observed  positions  of  the  earth  (that 
is,  the  earth's  own  positions  in  space)  must  also  be  in  the 
ecliptic.  They  are  therefore  included  in  a  plane. 


134        The  Earth  Revolves  Round  the  Sun 


Which  Way  is  the  Earth  traveling  ?  —  In  attempting  to 
pass  from  a  conception  of  the  earth  at  rest  as  it  seems,  to 
the  earth  moving  round  the  sun  as  it  really 
is,  no  help  can  be  greater  than  the  frequent 
pointing  toward  the  direction  in  which  the 
earth    is    actually   traveling.      The    gradual 
and  regular  variation  of  this  direction  with 
the  hours  of  day  and  night,   and  its   rela- 
tion to  fixed  lines  in  a 
room  or  building,  will 
soon     impress     firmly 
upon    the    mind    the    great  truth  of 
the    earth's    annual    motion 
round  the  sun. 

Extend  the  arms  at  right  angles 
to  each  other  as  in  the  illustration. 
Swing  round  until  the  left  arm  is 
pointed  toward  the  sun,  whether 
above  or  below  the  horizon.    This 
arm  will  then  be  in  the  plane 
of  the  ecliptic.     Still  keep- 
ing the  arms  at  right  angles,  bring 
the  right  arm  as  nearly  as  may  be      ""--^    ^ 
into  the  plane  of  the  ecliptic  at  the 
time.     This  may  be   done  as  al- 
ready indicated  on  page  67.      The   right   arm 
will  then  be  pointing  in  the  direction  in  which 
the  earth  is  journeying  in  space.     The  right  arm 
holding  the  ball  and  arrow  is  always  pointing  in 
the  direction  of  earth's  motion  through  space, 
relatively  to  the  local  horizon  in  the  latter  part 
of  September: 

(1)  at  6  A.M.,  upward  toward  a  point  about 
20°  south  of  the  zenith  ; 

(2)  at  noon,  toward  the  northwest,  at  an  alti- 
tude of  about  IO°  :  12  Noon  —  Earth  traveling 

(3)  at  6  p  M  ,  downward  to  a  point  about  20°  Westward 
below  the  north  horizon; 

(4)  at  midnight,  toward  the  northeast  at  an  altitude  of  about  10°. 


•—;-*—  ~— -  -**  ' 

f.      :    .  ,  .  \ 

6  A.M.  —  Earth  traveling  up 


Direction  of  Earth's  Motion 


135 


It  is  apparent  that  the  direction  of  the  earth's  motion  is  simply  the 

direction  of  a  point  whose  celestial  longitude  is  90°  less  than  that  of 

the  sun.    This  moving  point 

is   often    called    the   earth's 

goal,    or    the    apex    of    the 

ear  Hi's  way.  o^ 


Change    in    Absolute 
Direction    of    Earth's    Motion. —  In    an 

early  chapter  was  explained  how  east 
and  west,  north  and  south  at  a  given 
place  are  always  changing  with  the 
earth's  turning  on  its  axis,  and  that  it  is 
necessary  to  think  of  these  directions  as 
curving  round  with  the  surface  of  the 
earth.  We  saw,  too,  that  the  same  rela- 

.    ,        .,,          r  *•       i     6  P.M. —  Earth  traveling 

tions  exist  with  reference  to  the  cardinal  Downward 

points  of   the   celestial   sphere,   so  that 
east,  for  example,  in  one  part  of  the  heavens,  is  the  same 
absolute  direction  as  west  on   the   opposite    part   of   the 

celestial  sphere.     In  precisely 
the  same  way  we  have  now  to 
think  of  the  absolute  direction 
\  of  earth's  movement  round  the 
sun  as  continually  changing  in 
space.      If  at  one  moment  there  is  a  star 
exactly  toward  which  the  earth  is  trav- 
eling, three  months  before  that  time  and 
three  months  afterward  we  shall  be  going 
at  right  angles  to  a  line  from  the  sun  to 
that  star ;  and  six  months  from  the  given 
time  we  shall  be  traveling  exactly  away 
from  it.     In  the  chapter  relating  to  the 
stars  it  will  be  shown  how  this  motion  of 

12  Midnight  — Earth        ,  ,  n       t_        j 

traveling  Eastward     the   earth  in   space  can  actually  be  de- 


136        The  Earth  Revolves  Round  the  Sun 

monstrated  by  a  delicate  observation  with  an  instrument 
called  the  spectroscope. 

Earth's  Orbit  an  Ellipse.  —  The  angle  which  the  sun 
seems  to  fill,  as  seen  from  the  earth,  is  called  the  sun's 
apparent  diameter.  Measures  of  this  angle,  made  at 
intervals  of  a  few  days -throughout  the  year,  are  found  to 
differ  very  materially.  It  is  not  reasonable  to  suppose 
that  the  size  of  the  sun  itself  varies  in  this  manner. 
What,  then,  is  the  explanation  ?  Obviously  the  sun's  dis- 
tance from  us,  or,  what  is  the  same  thing,  our  distance 
from  him,  is  a  variable  quantity.  The  earth's  orbit,  then, 
cannot  be  a  circle,  unless  the  sun  is  out  of  its  center.  But 
the  observations  themselves,  if  carefully  made,  will  show 
the  true  shape  of  the  orbit.  It  is  not  necessary  to  know 
what  the  real  distance  of  the  sun  is,  because  we  are  here 
concerned  with  relative  distance  merely,  nor  need  the  ob- 
servations be  made  at  equal  intervals.  In  an  early  chapter 
we  saw  that  the  apparent  size  of  a  body  grows  less  as  its 
distance  becomes  greater.  Apply  this  principle  to  the 
measures  of  the  sun. 

Plot  the  observations  by  drawing  radial  lines  at  angles  corresponding 
to  various  directions  in  the  ecliptic  when  observations  of  the  sun's 
breadth  were  made.  Cut  off  the  radial  lines  at  distances  from  the 
radial  point  proportional  to  the  observed  diameters,  and  then  draw  a 
regular  curve  through  the  ends  of  the  radial  lines.  On  measuring  this 
curve,  it  is  found  that  it  deviates  only  slightly  from  a  circle,  but  that  it 
is  really  an  ellipse,  one  of  whose  foci  is  the  radial  point.  Earth's  orbit 
round  the  sun,  then,  is  an  ellipse,  with  the  sun  at  one  focus. 

The  Ellipse. — The  ellipse  is  a  closed  plane  curve,  ths 
sum  of  the  distances  from  every  point  of  which,  measured 
to  two  points  within  the  curve,  is  a  constant  quantity.  This 
constant  fixes  size  of  the  ellipse,  and  is  equal  to  its  longer 
axis,  or  major  axis  (figure  opposite).  At  right  angles  to 
the  major  axis,  and  through  its  center  is  the  minor  axis. 
The  two  determining  points  are  called  foci,  and  both  of 


Limits  of  the  Ellipse 


137 


Ellipse,  Foci,  Axes,  and  Radii  Vectores 


them   are   situated  in   the   major  axis,  at  equal  distances 

from  the  center  of  the  ellipse.     Divide  the  distance  from 

the  center  to  either  focus  by  the  half  of  the  major  axis, 

and  the  quotient  is  called 

the     eccentricity.       This 

quantity  fixes   the    form 

of   the    ellipse.      If    the 

foci  are  quite   near   the 

center,    the    eccentricity 

becomes  very  small,  and 

the  curve  approaches  the 

circle   in   form.      If   the 

center  and  both  foci  are 

merged  in  a  single  point,  evidently  the  ellipse  becomes  an 

actual  circle.     This  is  called  one  limit  of  the  ellipse.     But 

if  the  foci  recede  from  the  center  and  approach  very  near 

the  ends  of  the  major  axis,  then  the  corresponding  ellipse 

is   exceedingly  flattened;    and  its  limit   in   this   direction 

becomes  a  straight  line. 

Limits  of  the  Ellipse.  —  These  two  limits  are  easy  to 
illustrate,  practically,  by  looking  at  a  circular  disk  (a) 
perpendicularly,  and  (b)  edge  on.  In  tilting  it  90°  from 
one  position  to  the  other,  the  ellipse  passes  through  all 
possible  degrees  of  eccentricity.  The  orbits  of  the  heav- 
enly bodies  embrace  a  wide  range  of  eccentricity.  Some  of 
them  are  almost  perfectly  circular,  and  others  very  eccen- 
tric. In  drawing  figures  of  the  earth's  orbit,  the  flatten- 
ing is  necessarily  much  exaggerated,  and  this  fact  should 
always  be  kept  in  mind.  The  eccentricity  of  the  earth's 
orbit  is  about  •£$ ;  that  is,  the  sun's  distance  from  the 
center  of  the  orbit  is  only  g1^  part  of  the  semi-major  axis. 
If  it  is  desired  to  represent  the  earth's  orbit  in  true  pro- 
portions on  any  ordinary  scale,  the  usual  way  is  to  draw 
it  perfectly  circular,  and  then  set  the  focus  at  one  side  of 


138        The  Earth  Revolves  Round  the  Sun 


the  center,  and  distant  from  it  by  g1^  the  radius.  If  the 
center  is  obliterated,  a  well-practiced  eye  is  required  to 
detect  the  displacement  of  the  focus  from  the  center.  And 
as  we  shall  see,  many  of  the  celestial  orbits  are  even  more 
nearly  circular  than  ours. 

How  to  draw  an  Ellipse. —  The  definition  of  an  ellipse  suggests  at 
once  a  practical  method  of  drawing  it.  Lay  down  the  major  axis  and 
the  minor  axis.  From  either  extremity  of  the  latter,  with  a  radius  equal 
to  half  the  major  axis,  describe  a  circular  arc  cutting  the  major  axis  in 
two  parts.  These  will  be  the  foci.  Tie  together  the  ends  of  a  piece  of 
fine,  non-elastic  twine,  so  that  the  entire  length  of  the  loop  shall  be 

equal  to  the  major  axis  added 
to  the  distance  between  the 
foci.  Set  two  pins  in  the  foci, 
place  the  cord  around  them, 
and  carry  the  marking  point 
round  the  pins,  holding  the 
cord  all  the  time  taut.  The 
point  will  then  describe  an 
ellipse  with  sufficient  accuracy. 


Lines  and  Points  in  El- 

FIRST  OF 

ARIES      liptic  Orbits.  —  The  earth 


is  one  of  the  planets,  and 
in  treating  of  them  the 
laws  of  their  motion  in 
elliptic  orbits  will  be 
given.  In  a  still  later 
chapter  the  reason  why 
they  move  in  orbits  of 
this  character  will  be  ex- 
plained. Here  are  de- 
nned such  terms  as  are 
necessary  to  understand  in  dealing  with  the  earth.  Only 
one  of  the  foci  of  the  orbit  need  be  considered.  In  that  one 
the  primary  body  is  always  located.  Any  straight  line 
drawn  from  the  center  of  that  body,  as  S,  to  any  point  of 


Earth's  Orbit  (Ellipticity  much  exaggerated) 


Earth's  Orbit  in  t/ie  Future  139 

the  ellipse,  as  E,  is  called  a  radius  vector.  The  longest 
radius  vector  is  drawn  to  a  point  called  aphelion  ;  the  short- 
est radius  vector,  to  perihelion.  Together  these  two  radii 
vectores  make  up  the  major  axis  of  the  orbit.  Perihelion  is 
often  called  an  apsis ;  aphelion  also  is  called  an  apsis.  A 
line  of  indefinite  length  drawn  through  them,  or  simply  the 
major  axis  itself  unextended,  is  called  the  line  of  apsides. 
Imagine  the  point  where  the  line  of  apsides,  on  the  peri- 
helion side,  meets  the  celestial  sphere  to  be  represented  by 
a  star.  The  longitude  of  that  star,  or  its  angular  distance 
measured  counter-clockwise  from  the  first  of  Aries,  is  tech- 
nically called  the  longitude  of  perihelion.  This  is  100° 
in  the  case  of  the  earth.  The  longitude  of  perihelion  in- 
creases very  slowly  from  year  to  year ;  that  is,  the  apsides 
travel  eastward,  or  just  opposite  to  the  equinoxes.  But, 
slow  as  the  equinoxes  move,  the  apsides  travel  only  one 
fourth  as  fast. 

Earth's  Orbit  in  the  Future.  —  Not  only  does  the  line 
of  apsides  revolve,  but  the  obliquity  of  the  ecliptic  (page 
150)  changes  slightly,  and  even  the  eccentricity  of  the 
earth's  orbit  varies  slowly  from  age  to  age.  These  facts 
were  all  known  a  century  or  more  ago ;  but  with  regard 
to  the  eccentricity,  it  was  not  known  whether  it  might 
not  tend  to  go  on  increasing  for  ages.  Should  it  do  so, 
the  earth  would  be  parched  at  every  perihelion  passage, 
and  congealed  on  retreating  to  aphelion:  it  seemed  among 
the  possibilities  that  all  life  on  our  planet  might  thus  be 
destined  to  come  to  an  end,  although  remotely  in  the 
future.  But  in  the  latter  part  of  the  eighteenth  century, 
a  great  French  mathematician,  La  Grange,  discovered 
that  although  the  earth's  orbit  certainly  becomes  more  and 
more  eccentric  for  thousands  of  years,  this  process  must 
finally  stop,  and  it  then  begins  to  approach  more  and 
more  nearly  the  circular  form  during  the  following  period 


140        The  Earth  Revolves  Round  the  Sun 

of  thousands  of  years.  At  present  it  is  near  the  average 
value,  and  will  be  decreasing  for  the  next  24,000  years. 
He  showed,  too,  that  the  obliquity  of  the  ecliptic  simply 
fluctuates  through  a  narrow  range  on  either  side  of  an 
average  value.  These  slight  changes  are  technically 
called  secular  variations,  because  they  consume  very  long 
periods  of  time  in  completing  their  cycle.  The  mean  or 
average  distance,  and  with  it  the  time  of  revolution  round 
the  sun,  alone  remains  invariable.  As  we  know  this 
period  for  the  earth,  and  the  eccentricity  of  its  orbit 
together  with  the  location  of  its  perihelion  point,  by  cal- 
culating forward  or  backward  from  a  given  place  in  the 
sky  on  a  given  date,  we  can  find  the  position  of  the  sun 
(and  therefore  of  the  earth  in  its  orbit)  with  great  accu- 
racy for  any  past  or  future  time. 

Earth's  Motion  in  Orbit  not  Uniform.  —  Refer  back  to 
the  observations  of  the  sun's  diameter  by  which  it  was 
shown  that  our  orbit  round  the  sun  is  not  a  circle,  but  an 
ellipse.  Had  they  been  made  at  equal  intervals  of  time, 
it  would  at  once  have  been  seen,  on  plotting  them,  that 

the  angles  through  which 
the  radius  vector  travels 
are  not  only  unequal,  but 
that  they  are  largest  at 
perihelion,  and  smallest  at 
aphelion.  By  employing 
mathematical  processes, 

Radius  Vector  sweeps  Equal  Areas  in  it  is  easy  to  show  from  the 

Equal  Times  observations  of  diameter, 

connected  with  the  corresponding  angles,  that  a  definite 
law  governs  the  motion  of  the  earth  in  its  orbit.  Kepler 
was  the  first  astronomer  who  discovered  this  fact,  and 
from  him  it  is  called  Kepler's  law.  It  will  seem  remark- 
able until  one  apprehends  the  reason  underlying  it.  The 


The   Unit  of  Celestial  Measurement        141 

law  is  simply  this  :  The  radius  vector  passes  over  equal 
areas  in  equal  times.  That  the  figure  opposite  may  illus- 
trate this,  an  ellipse  is  drawn  of  much  greater  eccentricity 
than  any  real  planetary  orbit  has.  What  the  law  asserts  is 
this :  Suppose  that  in  a  given  time,  say  one  month,  the 
earth  in  different  parts  of  its  orbit  moves  over  arcs  equal 
to  the  arrows ;  then  the  lengths  of  these  arrows  are  so  pro- 
portioned that  their  corresponding  shaded  areas  are  all 
equal  to  each  other.  And  this  relation  holds  true  in  all 
parts  of  the  orbit,  no  matter  what  the  interval  of  time. 

The  Unit  of  Celestial  Measurement.  —  By  taking  the 
average  or  mean  of  all  the  radii  vectores,  a  line  is  found 
whose  length  is  equal  to  half  the  major  axis.  This  is 
called  the  mean  distance.  The  mean  distance  of  the 
center  of  the  earth  from  the  center  of  the  sun  we  shall 
next  find  from  the  velocity  of  light.  This  distance  is 
93,000,000  miles,  and  it  is  the  unit  of  measurement  uni- 
versally employed  in  the  astronomy  of  the  solar  system. 
Consequently,  it  is  often  called  distance  unity;  and  as 
other  distances  are  expressed  in  terms  of  it,  they  have 
only  to  be  multiplied  by  93,000,000,  to  express  them  in 
miles  also. 

Trying  to  conceive  of  this  inconceivable  distance  is  worth  the 
while.  Illustrations  sometimes  help.  Three  are  given  :  (a}  If  you  had 
silver  half  dollars,  one  for  every  mile  of  distance  from  the  earth  to  the 
sun,  they  would  fill  three  ordinary  freight  cars.  If  laid  edge  to  edge  in 
a  straight  line,  they  would  reach  from  Boston  to  Denver,  (b}  It  has  been 
found  by  experiment  that  the  electric  wave  in  ordinary  wires  travels  as 
far  as  from  New  York  to  Japan  and  back  in  a  single  second  (about 
16,000  miles).  If  you  were  to  call  up  a  friend  in  the  sun  by  telephone, 
the  cosmic  line  would  be  sure  to  prove  more  exasperating  than  terres- 
trial ones  sometimes  are ;  for  even  if  he  were  to  respond  at  once,  you 
would  have  to  wait  3'  hours.  (V)  Suppose  that  as  soon  as  George 
Washington  was  born,  he  could  have  started  for  the  sun  on  a  fast 
express  train,  like  the  one  illustrated  on  page  45,  which  can  make  long 
runs  at  the  rate  of  60  miles  an  hour.  Suppose,  too,  that  it  had  been 
keeping  up  this  speed  ever  since,  day  and  night,  without  stopping,  A 


142        The  Earth  Revolves  Round  the  Sun 

long,  long  time  to  travel  continuously,  but  his  body  would  still  be  on 
the  road,  for  the  train  would  not  reach  the  sun  till  1907. 

Finding  the  Velocity  of  Light  by  Experiment.  —  Light 
travels  from  one  part  of  the  universe  to  another  with 
inconceivable  rapidity.  Light  is  not  a  substance,  because 
experiment  proves  that  darkness  can  be  produced  by  the 
addition  of  two  portions  of  light.  Such  an  experiment  is 
not  possible  with  substances.  All  luminous  bodies  have 
the  power  of  producing  in  the  ether  a  species  of  wave 
motion.  The  ether  is  a  material  substance  which  fills  all 
space  and  the  interstices  of  all  bodies.  It  is  perfectly 
elastic  and  has  no  weight.  As  light  travels  by  setting  up 
very  rapid  vibrations  of  the  particles  of  the  ether,  it  is 
usually  called  the  luminiferous  ether.  Different  from  the 
vibrations  of  the  atmospheric  particles  in  a  sound  wave, 

light  waves  travel  by 
vibrations  of  the  ether 
athwart  the  course  of  the 
ray.  The  velocity  of  wave 

£  /  transmission  is  called  the 

S          /rn  velocity  of  light.     It  is  not 

difficult  to  find  by  actual 
experiment. 

One  method  is  illustrated  by 
the   figure.     A  ray  of  light    is 
thrown   into  the   instrument   at 
Bj  in  the  direction  of  the  dotted 
line.     It  is   reflected  at  C,  and 
goes  out  of  the  telescope  A  to 
a  distant  mirror,  which  reflects 
it  directly  back  to  the  telescope 
Finding  Velocity  of  Light        again,  and  the  observer  catches 
•   the  return  ray  by  placing  the  eye 

at  D.  In  the  field  of  the  telescope  are  the  teeth  of  a  wheel  E,  through 
which  outgoing  and  returning  rays  must  pass.  With  the  wheel  at  rest, 
the  return  ray  is  fully  seen  between  the  teeth  of  the  wheel.  Whirl  the 


Size  of  the  Earth's  Orbit  143 

wheel  rapidly.  While  the  direct  ray  is  going  out  to  the  mirror  and 
coming  back  to  the  wheel,  a  tooth  will  have  moved  partly  over  its  own 
width,  and  will  therefore  partly  shut  off  the  ray,  so  that  the  star  appears 
faint  instead  of  light.  Whirl  the  wheel  faster,  and  the  return  ray  be- 
comes invisible.  Keep  on  increasing  the  velocity  of  the  wheel,  and  the 
star  again  reappears  gradually.  And  so  on.  More  than  twenty  disap- 
pearances and  reappearances  can  be  observed.  The  speed  of  the  wheel 
is  known,  because  its  revolutions  are  registered  automatically  by  the 
driving  apparatus  (omitted  in  the  figure)  ;  and  the  distance  of  the  mir- 
ror from  the  wheel  can  be  accurately  measured,  so  that  the  velocity  of 
light  can  be  calculated. 

This  and  other  similar  experiments  have  often  been 
repeated  by  Cornu,  Michelson,  Newcomb,  and  others,  in 
Europe  and  America ;  and  the  result  of  combining  them 
all  is  that  light  waves,  regardless  of  their  color,  travel 
186,300  miles  in  a  second  of  time. 

Size  of  the  Earth's  Orbit. — Where  matters  pertaining 
to  elementary  explanation  are  simplified  by  so  doing,  it  is 
evident  that  the  earth's  orbit  may  be  regarded  as  a  circle. 
From  several  hundred  years'  observation  of  the  moons 
which  travel  round  the  planet  Jupiter,  it  has  been  found 
that  reflected  sunlight  by  which  we  see  them  consumes 
998  seconds  in  traveling  across  a  diameter  of  the  earth's 
orbit  (page  345).  So  that  \  x  998  x  186,300  is  the  radius 
of  that  orbit,  or  the  mean  distance  of  the  sun.  This 
distance  is  93,000,000  miles,  just  given.  Earth  is  at 
perihelion  about  the  1st  of  January  each  year,  and  on 
account  of  eccentricity  of  our  orbit  we  are  about  3,000,000 
miles  nearer  the  sun  on  the  ist  of  January  than  on  the 
ist  of  July.  Our  globe  travels  all  the  way  round  this 
vast  orbit,  from  perihelion  back  to  perihelion  again,  in 
the  course  of  a  calendar  year.  Clearly,  its  motion  must 
be  very  swift.  Hold  a  penny  between  the  fingers  at  a 
height  of  four  feet.  Suddenly  let  it  drop:  in  just  a  half 
second  it  will  reach  the  floor.  So  swiftly  are  we  traveling 
in  our  orbit  round  the  sun,  that  in  this  brief  half  second 


144        The  Earth  Revolves  Round  the  Sun 


we  have  sped  onward  9^  miles.  And  in  all  other  half 
seconds,  whether  day  or  night,  through  all  the  weeks  and 
months  of  the  year,  this  almost  inconceivable  speed  is 
maintained. 

Earth's  Deviation  from  a  Straight  Line  in  One  Second.— 
As  our  distance  from  the  sun  is  approximately  93,000,000 
miles,  the  circumference  of  our  orbit  round  him  (consid- 
ered as  a  circle)  is  584,600,000  miles.     But  as  we  shall 

see  in  a  later  paragraph,  the 
earth  goes  completely  round 
the  sun  in  one  sidereal  year, 
or  365  d.  6  h.  9  m.  9  s. ;  there- 
fore in  one  second  our  globe 
travels  through  space  i8|- 
miles.  In  that  short  interval, 
how  far  does  our  path  bend 
away  from  a  straight  line,  or 
tangent  to  the  orbit  ?  Sup- 
pose that  in  one  second  of 
time,  the  earth  would  move 
in  a  straight  line  from  M 
to  TV,  if  the  sun  exerted  no 
attraction  upon  us.  Because 
of  this  attraction,  however,  we 
travel  over  the  arc  Mn.  The  length  of  this  arc  is  18^ 
miles,  or  about  0^.04  as  seen  from  the  sun  ;  and  as  this 
angle  is  very  small,  the  arc  Mn  may  be  regarded  as  a 
straight  line,  so  that  MnU 'is  a  right  angle.  Therefore 

MU:  Mn::  Mn:  Mm 

But  MU  is  double  our  distance  from  the  sun;  therefore 
Mm  is  0.119  inch,  which  is  equal  to  Nn,  or  the  distance 
the  earth  falls  from  a  straight  line  in  one  second.  So 
that  we  reach  this  very  remarkable  result :  The  curvature 


Earth's  Deviation  in  One  Second 


Solar  and  Sidereal  Day  145 

of  our  path  round  the  sun  is  such  that  in  going  i8£ 
miles  we  deviate  from  a  straight  line  by  only  -J-  of  an 
inch. 

Reason  for  the  Difference  between  Solar  and  Sidereal 
Day.  —  The  real  reason  why  the  sidereal  day  is  shorter 
than  the  solar  day  can  now  be  made  clear.  The  figure  is 
a  help.  If  earth  were  not  moving  round  the  sun,  but 
standing  still  in  space,  one  sidereal  day  would  be  the  time 
consumed  by  a  point  on  the  equator,  A,  in  going  all  the  way 


Sidereal  and  Solar  Day  compared 

round  in  direction  of  the  lower  arrows,  and  returning  to 
the  point  of  starting.  But  while  one  sidereal  day  is  elaps- 
ing, the  earth  is  speeding  eastward  in  its  orbit,  from  O  to  O' . 
Sun  and  star  were  both  in  the  direction  AS  at  the  begin- 
ning; but  after  the  earth  has  turned  completely  round, 
the  star  will  be  seen  in  the  direction  O'A,  which  is  par- 
allel to  OA,  because  OOf  is  an  indefinitely  small  part  of 
the  whole  distance  of  the  star.  This  marks  one  sidereal 
TODD'S  ASTRON.  — 10 


146        The  Earth  Revolves  Round  the  Sun 

day.  The  sun,  however,  is  in  the  direction  Of  S ;  and  the 
solar  day  is  not  complete  until  the  earth  has  turned  round 
on  its  axis  enough  farther  to  bring  A  underneath  5.  This 
requires  nearly  four  minutes ;  so  the  length  of  the  solar 
day  is  24  hours  of  solar  time,  while  the  sidereal  day,  or 
real  period  of  the  earth's  rotation,  equals  23  h.  56  m'.  4.09  s. 
of  solar  time.  Also  in  the  ordinary  year  of  365^  solar 
days,  there  are  366^  sidereal  days. 

Sun's  Yearly  Motion  North  and  South. — You  have  found 
out  the  eastward  motion  of  the  sun  among  the  stars  from 
the  fact  that  they  are  observed  to  be  farther  and  farther 


Direction  of  Sun's  Rays  at  Equinoxes  and  Solstices 

west  at  a  given  hour  each  night.  You  must  next  ascer- 
tain the  nature  of  the  sun's  motion  north  and  south.  The 
most  convenient  way  will  be  to  observe  where  the  noon 
shadow  of  the  top  of  some  pointed  object  falls.  Begin 
at  any  time  of  the  year;  in  autumn,  for  example.  This 
shadow  will  grow  longer  and  longer  each  day ;  that  is,  the 
noonday  sun  is  getting  lower  and  lower  down  from  the 
zenith  toward  the  south.  How  low  will  it  actually  go  ? 
And  when  is  this  epoch  of  greatest  length  of  the  shadow  ? 
Even  the  crudest  observation  shows  that  the  noonday 


The  Suns   Yearly  Motion  North  147 

shadow  will  continue  lengthening  till  the  2Oth  of  Decem- 
ber; but  the  daily  increase  of  its  length  just  before  that 
date  will  be  difficult  to  observe,  it  is  so  very  slight.  Then 
for  a  few  days  there  will  be  no  perceptible  change ;  in  so 
far  as  motion  north  or  south  is  concerned,  the  sun  appears 
to  stand  still.  As  this  circumstance  was  the  origin  of  the 
name  solstice,  notice  that  it  indicates  both  time  and  space : 
the  winter  solstice  is  the  time  when  (or  the  point  in  the 
celestial  sphere  ivhere}  the  sun  appears  to  '  stand  still '  at 
its  greatest  declination  south.  The  time  is  about  the  2Oth 
of  December.  Not  until  after  Christmas  will  it  be  possible 
to  observe  the  sun  moving  north  again ;  and  then,  at  first, 
by  a  very  small  amount  each  day. 

The  Sun  in  Midwinter.  —  For  the  sake  of  comparison 
with  other  days  in  the  year,  let  us  photograph  (at  noon 
on  a  bright  day  near  the  winter  solstice)  some  familiar 
object  with  a  south  exposure;  for  example,  a  small  and 
slender  tree,  with  its  shadow  (next  page).  Observe  how 
much  shorter  tree  is  than  shadow,  because  the  sun  culmi- 
nates low.  So  far  north  does  the  shadow  of  the  tree  fall 
that  a  part  of  it  actually  reached  the  house  where  the  camera 
stood.  Verify  the  northeast-by-east  direction  of  the  sunset 
shadow  of  the  tree  ;  and  the  corresponding  direction  (north- 
west-by-west)  of  its  sunrise  shadow,  also ;  for  the  sun  will 
now  rise  at  a  more  available  hour  than  in  midsummer. 
Notice,  too,  how  sharply  defined  the  shadow  is,  near  the 
trunk  of  the  tree ;  and  how  ill-defined  the  shadows  of  the 
branches  are.  This  is  because  the  sun's  light  comes  from 
a  disk,  not  a  point ;  the  shadows  are  penumbral,  that  is, 
not  quite  like  dark  shadows ;  and  they  grow  more  and 
more  hazy,  the  farther  the  surface  upon  which  they  fall. 

The  Sun's  Yearly  Motion  North.  —  Onward  from  the 
beginning  of  the  year,  continue  to  watch  the  sun's  slow 
march  northward.  With  each  day  its  noontime  shadow 


148        The  Earth  Revolves  Round  the  Sun 


will  grow  shorter  and  shorter.  Watch  the  point  in  the 
western  horizon  where  the  sun  sets ;  with  each  day  this, 
too,  is  coming  farther  and  farther  north.  Note  the  day 

when  the  sun  sets  ex- 
actly in  the  west ;  this 
will  be  about  the  2Oth 
of  March.  As  the 
sun  sets  due  west, 
evidently  it  must  pre- 
viously have  risen  due 
east ;  therefore  the 
great  circle  of  its 
diurnal  motion  (which 
at  this  season  is  the 
equator)  must  be  bi- 
sected by  the  horizon. 
Day  and  night,  then, 
are  of  equal  hngth. 
The  vernal  equinox  is 
the  time  when  (or  the 
point  where)  the  sun 
going  northward 
crosses  the  celestial 
equator. 

The  Sun  in  Mid- 
summer. —  Now  be- 
gin again  the  obser- 
vations of  the  noon- 
time shadow.  Shorter 
and  shorter  it  grows  and  perceptibly  so  each  day.  But  it 
will  be  noticed  that  the  difference  from  day  to  day  is  less 
than  the  daily  increase  of  length  six  months  before.  That 
is  simply  because  the  shadows  fall  nearer  the  tree,  and  are 
measured  more  nearly  at  right  angles  to  the  sun's  direction 


Midwinter  Shadows  Longest 


The  Sun  in  Midsummer 


149 


than  they  were  in  the  autumn  and  winter.     The  azimuth 
of  its  setting  will  increase.     How  many  weeks  will  the 
length  of  the  shadow  continue  to  decrease  ?     How  short 
will  it  actually  get  ?     About  the  middle  of  June,  it  will  be 
almost   impossible  to 
notice  any  further  de- 
crease   in   the    shad- 
ow's  length,  and   on 
2Oth    June    we    may 
again    photograph 
the   same   tree.     But 
how  changed !      The 
short    shadow  of    its 
trunk   is   all    merged 
in     the     shadow     of 
the  foliage   where   it 
falls  upon  the  lawn. 
Points  of  the  compass 
alone  are  unchanged. 
Here    again    at   mid- 
summer,    the     sun 
stands  still,  and  there 
is  a   second   solstice. 
Summer     solstice    is 
the    time    when    (or 
the  point  on  the  celestial  sphere  where)  the  sun  appears 
to  '  stand  still '  at  greatest  declination  north.     Do  not  fail 
to  notice  the  points  of  the  compass.     Also  verify  at  mid- 
summer the  indicated  direction  (southeast-by-east)  in  which 
the  tree's  shadow  falls  at  sunset ;  and  near  the  beginning 
of  the  summer  vacation  it  will  be  worth  while  to  arise  once 
at  five  o'clock  in  the  morning,  in  order  to  verify  also  the 
southwest-by-west  direction  of  the  shadow  just  after  sun- 
rise.    By  the  latter  part  of  June,  the   noontime    shadow 


Midsummer  Shadows  Shortest 


150        The  Earth  Revolves  Round  the  Sun 

again  begins  to  lengthen ;  more  and  more  rapidly  with 
each  day  it  lengthens  until  the  equinox  of  autumn,  when 
the  cycle  of  one  year  of  observation  is  complete. 

To  observe  the  Inclination  of  Equator  to  Ecliptic.  —  As  equator  and 
ecliptic  are  both  great  circles,  the  sun  goes  as  far  north  in  summer  as 
it  goes  south  in  winter.  Half  the  extreme  range  is  the  angle  of  incli- 
nation of  ecliptic  to  equator,  and  it  is  technically  termed  the  obliquity 
of  the  ecliptic.  Its  value  for  1900  is  23°  27'  8". 02,  and  it  changes  very 
slowly.  A  rough  value  is  readily  found  for  any  year  by  making  use  of 
the  latitude-box  already  described  on  page  82.  At  noon  on  the  2oth, 
2  ist,  and  22d  of  December,  observe  the  readings  on  the  arc  where 
the  sun's  line  falls.  Be  sure  that  the  box  remains  undisturbed,  or  test 
the  vertical  arm  of  the  quadrant  by  the  plumb-line  each  day.  Leave  the 
box  in  position  through  the  winter  and  spring,  or  set  up  the  same  box 
again  in  June,  and  again  apply  the  plumb-line  test.  At  noon  on  the 
20th,  2 ist,  and  22d  of  June,  observe  the  sun's  reading  as  at  the  other 
solstice.  Take  the  difference  of  readings  as  follows  :  — 

Reading  of  22d  December  from  2oth  June ; 
2 ist  December  from  2 ist  June  ; 
2oth  December  from  22d  June. 

Then  halve  each  of  the  three  differences,  and  the  results  will  be  three 
values  for  the  inclination  of  equator  to  ecliptic.  Take  the  average  of 
them  for  your  final  value.  Thus  in  about  six  months'  time  you  will 
have  all  the  observations  needed  for  a  new  value  of  the  obliquity  of 
the  ecliptic.  True,  its  accuracy  may  not  be  such  that  the  government 
astronomers  will  ask  to  use  it  in  place  of  the  refined  determinations  of 
Le  Verrier  and  Hansen,  but  your  practical  knowledge  of  an  elementary 
principle  by  which  the  obliquity  is  found  will  be  worth  the  having. 

Following  are  readings  made  in  this  manner  at  Am- 
herst,  Massachusetts :  — 

ARC-READING  ARC-READING  OBLIQUITY 

June  20,  7i°.2          Subtract  December  22,    24°. 3  =  46°. 9  23°-45 

21,71.0  21,    24.0  =  47.0  23.5 

22,  70  .9  20,    24  .  i  =  46  .8  23  .4 

Mean  value  of  obliquity  =  23°  27' 

Explanation  of  the  Equation  of  Time.  —  The  reason  may 
now  be  apprehended  why  mean  sun  and  real  sun  seldom 


Explanation  of  Equation  of  Time         1 5 1 


MEAN  SUN   IS  HERE 


cross  the  meridian  together.  It  is  chiefly  due  to  two  inde- 
pendent causes,  (i)  The  orbit  in  which  our  earth  travels 
round  the  sun  is  an  ellipse.  Motion  in  it  is  variable  — 
swiftest  about  the  ist  of  January,  and  slowest  about  the 
ist  of  July.  On  these  dates,  the  equation  of  time  due 
to  this  cause  vanishes.  Nearly  intermediate  it  has  a  mean 
rate  of  motion;  therefore  at  these  times  (about  ist  April 
and  ist  October), 
the  true  sun  and 
the  fictitious  sun 
must  both  travel 
at  the  same  rate  in 
the  heavens.  But 
the  real  sun  has 
been  running  ahead 
all  the  time  since 
the  beginning  of 
the  year,  as  this 
figure  shows ;  so 
that  on  the  ist  of  April,  the  equation  of  time,  from  this 
cause  alone,  is  eight  minutes.  The  sun  is  slow  by  this 
amount  because  it  has  been  traveling  eastward  so  rapidly. 
On  ist  October  it  is  fast  a  like  amount,  because  it  has 
been  moving  very  slowly  through  aphelion  in  the  summer 
months ;  therefore  the  real  sun  comes  to  the  meridian 
earlier  than  it  should,  and  it  is  said  to  be  fast. 

(2)  The  second  cause  is  the  obliquity  of  the  ecliptic. 
Suppose  that  the  sun's  apparent  motion  in  the  ecliptic 
were  uniform  :  near  the  solstices  its  right  ascension  would 
increase  most  rapidly,  because  the  hour  circles  converge 
toward  the  celestial  poles  just  as  meridians  do  on  the  earth. 
The  case  is  like  that  of  a  ship  sailing  due  east  or  west  at 
a  uniform  speed  :  when  in  high  latitudes  she  '  makes  longi- 
tude '  much  faster  than  she  does  near  the  equator.  As 


_ 

AMONG    - 

Relation  of  True  Sun  to  Mean  Sun 


152        The  Earth  Revolves  Round  the  Sun 

due  to  the  second  cause  the  equation  of  time  vanishes  four 
times  a  year ;  twice  at  the  equinoxes  and  twice  at  the  sol- 
stices. At  intermediate  points  (about  the  8th  of  February, 
May,  August,  and  November),  the  sun  is  alternately  slow 
and  fast  about  10  minutes.  Combining  both  causes  gives 
the  equation  of  time  as  already  presented  in  the  table  on 
page  113.  It  is  zero  on  I5th  April,  I4th  June,  1st  Sep- 
tember, and  24th  December.  The  sun  is  slowest  (14^ 
minutes)  about  nth  February,  and  fastest  (16^  minutes) 
about  2d  November.  Attention  is  next  in  order  turned  to 
that  remarkable  yearly  variation  in  conditions  of  heat 
and  cold  in  our  latitudes,  called  the  seasons. 

The  Seasons  in  General.  —  Those  great  changes  in  outward  nature 
which  we  call  the  seasons  are  by  no  means  equally  pronounced  every- 
where throughout  our  extended  country.  It  is  well,  therefore,  to 
sketch  them  in  outline,  from  a  naturalist's  point  of  view,  which  is  quite 
different  from  that  of  the  astronomer.  The  earliest  peoples  noted 


Plane    of  Ecliptic 


Pole 

Earth's  Axis  inclined  66i°  to  the  Plane  of  its  Orbit 

these  variations  for  practical  purposes,  chiefly  seedtime  and  harvest. 
But  as  men  grew  past  the  necessities  of  mere  living,  they  began  to  ob- 
serve the  natural  beauty  of  each  season  as  it  came.  Not  knowing  what 
occasioned  the  unvarying  succession  of  these  fixed,  yet  widely  different 
conditions  of  the  year,  all  sorts  of  fanciful  explanations  were  invented. 
Clearly  it  is  not  the  simple  nearness  or  distance  of  the  sun,  as  we  ap- 
proach or  recede  in  our  orbit,  which  causes  our  changing  seasons, 
for  in  our  winter  we  are,  as  has  already  been  said,  3,000,000  miles 
nearer  than  in  summer.  But  as  earth  passes  round  the  sun  in  its  yearly 
path,  the  axis  remains  always  from  year  to  year  practically  parallel  to 
itself  in  space  (neglecting  the  effect  of  precession),  its  inclination  to  the 
ecliptic  being  66£°  as  shown  in  the  outline  figure  above.  Alternately, 
then,  the  poles  of  earth  are  tilted  toward  and  from  that  all-potent  and 
heat-  giving  luminary.  So  in  the  sunward  hemisphere  summer  pre- 
va'ls  because  of  accumulated  heat  :  more  is  received  each  day  than  is 


The  Seasons  153 

lost  by  radiation  each  night.  But  in  the  hemisphere  turned  away  from 
the  sun  for  the  time,  gradually  temperature  is  lowered  by  withdrawal  of 
life-giving  warmth,  more  and  more  each  day.  Medium  temperatures 
of  autumn  follow,  and  eventually  it  becomes  midwinter. 

Spring  and  Summer.  —  But  when,  by  the  earth's  journeying  onward 
in  its  orbital  round,  the  pole  again  becomes  tilted  more  and  more  to- 
ward the  sun,  soon  an  awakening  begins.  The  melting  of  ice  and 
snow,  the  gradual  reviving  of  brown  sods,  the  flowing  of  sap  through 
branches  apparently  lifeless,  the  mist  of  foliage  beginning  to  enshroud 
every  twig  until  the  whole  country  is  enveloped  in  a  soft  haze  of  palest 
green  and  red,  gray  and  yellow, : —  all  these  are  Nature's  signs  of  spring. 
Biologists  tell  us  that  this  vegetal  awakening  comes  when  the  tem- 
perature reaches  44°  Fahrenheit.  Soon  come  the  higher  temperatures 
requisite  for  more  mature  development,  and  midsummer  follows  rapidly. 
The  astronomer  can,  of  course,  say  just  when  in  June  our  longest  day 
comes  —  when  the  sun  rises  farthest  north  and  sets  farthest  north, 
thereby  shining  more  nearly  vertically  upon  us  at  noon,  and  remaining 
above  the  horizon  as  long  as  possible;  when  daylight  lasts  with  us 
until  long  past  eight  o'clock,  and  in  England  and  Scotland  until  nearly 
ten.  But  who  can  divine  just  when  the  country  stands  at  the  fullest 
flood  tide  of  summer,  with  the  rich  growth  of  vegetation,  tangled 
masses  of  flowers  and  foliage,  roadsides  crowded  with  beauty,  the 
shimmer  of  heat  above  ripening  fields,  perfecting  grains,  and  early 
fruits  ?  Or  when  it  first  begins  to  ebb  ?  That  is  for  another  observer 
no  less  subtile  than  the  astronomer  with  his  measuring  instruments  and 
geometric  demonstrations.  Very  different,  too,  is  the  time  in  different 
places ;  often  there  is  a  wide  range  of  local  conditions  which  modify 
greatly  the  effects  produced  by  purely  astronomical  causes. 

Autumn  and  Winter.  —  Thoreau,  that  keen  observer  of  times  and 
seasons,  used  always  to  detect  signs  of  summer's  waning  in  early  July. 
But  persons  in  general  notice  few  of  the  advance  signals  of  a  dying 
year.  Not  until  falling  leaves  begin  to  flutter  about  their  feet,  and 
grapes  and  apples  ripen  in  orchard  and  vineyard,  do  they  realize  that 
autumn  is  really  here  —  that  season  of  fulfillment,  when  everything  is 
mellow  and  finished.  Our  hemisphere  of  the  earth  is  turning  yet 
farther  away  from  that  sun  upon  which  all  growth  and  development 
depend.  When  trees  are  a  glory  of  red  and  yellow  and  russet  brown, 
when  corn  stands  in  full  shocks  in  fields,  and  day  after  day  of  warmth 
and  sunshine  follow  through  royal  October,  —  it  seems  impossible  to 
believe  that  slowly  and  surely,  winter  can  be  approaching.  But  soon 
chilly  winds  whistle  through  trees  from  which  the  bright  leaves  are 
almost  gone ;  a  thin  skim  of  ice  crystals  shoots  across  wayside  pools 
at  evening,  and  speedily  shivering  winter  is  upon  us.  Just  before 
Christmas,  this  part  of  our  earth  is  tipped  its  farthest  away  from  the 


154        The  Earth  Revolves  Round  the  Sun 

sun.  Then,  for  a  few  days,  the  hours  of  darkness  are  at  their  longest. 
The  sap  has  withdrawn  far  into  the  roots  of  trees  until  the  cold  shall 
abate ;  leaden  skies  drop  snowflakes,  and  earth  sleeps  under  a  mantle 
of  white.  Cold  is  apt  to  increase  for  a  month  after  the  sun  has  actually 
begun  to  journey  northward.  His  rays,  warm  and  brilliant,  flood  every 
nook  and  crevice  in  leafless  forests ;  but  where  is  their  mysterious 
power  to  call  life  into  bare  branches,  to  wake  the  flowers,  and  stir  the 
grass?  It  is  almost  startling  to  think  that  a  permanent  withdrawal  of 
even  a  slight  amount  of  the  sun's  warmth  would  freeze  this  fair  earth 
into  perpetual  winter — that  a  small  change  in  the  tilt  of  our  axis 
might  make  arctic  regions  where  now  the  beauty  of  summer  reigns  in 
its  turn.  But  the  laws  of  the  universe  insure  its  stability  ;  and  changes 
of  movement  or  direction  are  very  slow  and  gradual,  so  that  all  our 
familiar  variation  of  seasons,  each  with  its  own  charm,  cannot  fail  to 
continue  for  more  years  than  it  is  possible  to  apprehend.  In  late  Janu- 
ary, weeks  after  our  hemisphere  has  begun  again  to  turn  sunward,  even 
the  most  careless  observer  notes  the  lengthening  hours  of  daylight,  and 
knows  that  spring  is  coming.  That  thrill  of  mysterious  life  which  this 
earth  feels  at  greater  warmth,  and  the  quiet  acceptance  of  its  with- 
drawal, have  been  celebrated  by  poets  in  all  ages  ;  and  the  astronomer's 
explanations  of  whys  and  wherefores  cannot  add  to  these  marvelous 
changes  anything  of  beauty  or  perennial  interest,  although  they  may 
conduce  to  completeness  and  precision  of  statement. 

Explanation  of  the  Change  of  Seasons.  —  So  much  for 
mere  description  :  the  explanation  has  already  been  hinted. 
Our  change  of  season  is  due  to  obliquity  of  the  ecliptic, 
or  to  the  fact  that  the  axis  of  our  planet,  as  it  travels  round 
the  sun,  keeps  parallel  to  itself,  and  constantly  inclined  to 
its  orbit-plane  by  an  angle  of  66-|°.  The  opposite  illustra- 
tion should  help  to  make  this  clear. 

Beginning  at  the  bottom  of  the  figure,  or  at  midsummer,  it  is  appar- 
ent how  the  earth's  northern  pole  is  tilted  toward  the  sun  by  the  full 
amount  of  the  obliquity,  or  23^°.  It  is  midsummer  in  the  northern 
hemisphere,  also  it  is  winter  in  the  southern,  because  the  south  pole  is 
obviously  turned  away  from  the  sun.  Passing  round  to  autumn,  in 
the  direction  of  the  large  arrows,  reason  for  the  equable  temperatures 
of  that  season  is  at  once  apparent :  it  is  the  time  of  the  autumnal  equi- 
nox, or  of  equal  day  and  night  everywhere  on  the  earth,  and  the  sun's 
rays  just  reach  both  poles.  Going  still  farther  round  in  the  same  direc- 
tion, to  the  top  of  the  illustration,  the  winter  solstice  is  reached ;  it  is 


Most  Heat  at  Midday 


155. 


northern  winter  because  the  north  pole  is  turned  away  from  the  sun 
and  can  receive  neither  light  nor  heat  therefrom  ;  also  the  southern  hem- 
isphere is  then  enjoying  summer,  because  the  south  pole  is  turned  23^° 
toward  the  sun.  Again  moving  quarter  way  round,  to  the  left  side  of  the 
illustration,  the  season  of  spring  is  accounted  for,  and  the  temperature 
is  equable  because  it  is  now  the  vernal  equinox.  Another  quarter 
year,  or  three  months,  finds  the  earth  returned  to  the  summer  solstice  ; 
and  so  the  round  of  seasons  runs  in  never-ending  cycle. 


UTU'MNAL  on    FIRST 
:~~—,ZC       I  OF  ARIES 


View  of  Earth's  Orbit  from  the  North  Pole  of  the  Ecliptic 

Earth  receives  most  Heat  at  Midday.  —  It  is  necessary  to 
examine  into  the  detail  of  these  changes  of  light  and  heat 
a  little  more  fully.  Every  one  is  aware  how  much  warmer 
it  usually  is  at  noon  than  at  sunrise  or  sunset,  mostly  be- 
cause of  change  in  inclination  of  the  sun's  rays  from  one 
time  of  day  to  another.  Any  surface  becomes  the  warmer. 


156        The  Earth  Revolves  Round  the  Sun 


the  more  nearly  perpendicularly  the  sun's  rays  strike  it, 
simply  because  more  rays  fall  upon  it. 

In  the  figure,  ab,  cd,  and  ef  are  equal  spaces,  and  R  is  the  bundle 
of  solar  rays  falling  upon  them.  Obviously  more  rays  fall  upon  cd  than 
upon  ab,  because  the  rays  are  parallel.  But  the 
lessened  warmth  of  sunrise  and  sunset  is  partly 
due  to  greater  absorption  of  solar  heat  by  our 
atmosphere  at  times  when  the  sun  is  rising  and 
setting,  because  its  rays  must  then  penetrate 
a  much  greater  thickness  of  the  air  than  at 
noon.  Suppose  the  observer  to  be  located 
within  the  tropics,  because  there  the  sun's  rays 
may  be  perpendicular  to  the  earth's  surface,  as 
shown  in  the  diagram  below,  while  in  our  lati- 
tudes they  never  can  be  quite  vertical  even  at 
midsummer  noon.  There  the  sun's  rays  may 
travel  vertica'iy  downward  at  apparent  noon;  and  it  is  evident  from 
•the  illustration  that  a  beam  of  sunlight  of  a  given  width  KL  traverses 
only  that  relatively  small  part  of  the  earth's  atmosphere  included  be- 
tween KL,  MN.  Now  at  sunrise  observe  the  different  conditions  under 
which  a  beam  of  sunlight  of  the  same  breadth  as  KL  is  obliged  to  trav- 
erse the  atmosphere.  Observe,  too,  how  much  more  atmosphere 
ABCD  this  beam  must  pass  through.  As  the  sun's  energy  is  absorbed 


A  Surface  receives  most 
Rays  when  th«v  fall 
Perpendicularly  upon 
it 


WEST 


The  Solar  Beams  are  spread  out  and  absorbed  at  Sunrise  and  Sunset 

in  heating  this  greater  volume  of  air,  evidently  the  amount  of  heat  arriv- 
ing at  the  earth's  surface,  CD,  where  we  are  directly  conscious  of  it, 
must  be  less  by  the  amount  which  the  atmosphere  has  absorbed.  Be- 
sides this  the  amount  of  solar  heat  which  falls  upon  a  given  area  between 
C  and  D  will  evidently  be  less  than  that  received  by  an  equal  area  be- 
tween M  and  N,  in  proportion  as  CD  is  greater  than  MN.  Like  con- 
ditions prevail  at  sunset  as  shown. 


The  United  States  as  seen  from  the  Sun 
in  Midwinter 


Most  Heat  at  the  Summer  Solstice         1 

Our  Latitudes  receive  most  Heat  at  the  Summer  Sol- 
stice. —  In  an  earlier  chapter  it  was  explained  how  the 
sun,  by  its  motion  north,  crosses  higher  and  higher  on 
our  meridian  every  day,  from  the  winter  solstice  to  the 
summer  solstice.  Just  as 
each  day  the  heat  received 
increases  from  sunrise  to 
noon,  and  then  decreases  to 
sunset,  so  the  heat  received 
at  noon  in  a  given  place  of 
middle  north  latitude,  increases  from  the  winter  solstice  to  a 
maximum  at  the  summer  solstice.  Also  the  sun's  diurnal  arc 
has  all  this  time  been  increasing,  so  that  a  given  hour  of 
the  morning,  as  nine  o'clock,  and  a  given  hour  of  the  after- 
noon, as  three  o'clock,  places  the  sun  higher  and  higher. 
The  heat  received,  then,  increases  for  two  independent 
though  connected  reasons:  (i)  the  sun  culminates  higher 
each  day,  and  (2)  it  is  above  the  horizon  longer  each  day. 
The  illustration  (page  30)  makes  both  reasons  clear.  The 

greater  length  of  daytime 
exerts  a  powerful  influence 
in  modifying  the  summer 
temperatures  of  regions  in 
very  high  latitudes  where 
the  summer  sun  shines  con- 
tinually through  the  24 
hours.  For  example,  at  the 

The  United  States  as  seen  from  the  Sun      summer      Solstice,     the      SUn 
in  Midsummer  .  1-1 

pours  down,  during  the  24 

hours,  one  fifth  more  heat  upon  the  north  pole  than  upon 
the  equator,  where  it  shines  but  12  hours.  So  it  is  not 
easy  to  calculate  the  relative  heat  received  at  different 
latitudes,  even  if  we  neglect  absorption  by  the  atmos- 
phere. With  this  effect  included,  the  problem  becomes 


158        The  Earth  Revolves  Round  the  Sun 


$2.50 


FIRST  WEEK 


SECOND  WEEK 


THIRD  WEEK 


more  complicated  still.  If  earth  and  atmosphere  could 
retain  all  the  heat  the  sun  pours  down  upon  them,  the 
summer  solstice  would  mark  also  the  time  of  greatest 
heat.  But  in  our  latitudes  radiation  of  heat  into  space 
retards  the  time  of  greatest  accumulated  heat  more  than 
a  month  after  the  summer  solstice.  For  evidently  the 
atmosphere  and  the  earth  are  storing  heat  so  long  as  the 
daily  quantity  received  exceeds  the  loss  by  radiation.  For 
a  similar  reason,  the  time  of  greatest  cold,  or  withdrawal 
of  warmth,  is  not  coincident  with  the  winter  solstice,  but 
lags  till  the  latter  part  of  January. 

Accumulation   ceases   when    Loss   equals   Gain.  —  Illustration   by  a 
three  weeks1  petty  cash  account  should  make  this  apparent.     You  start 

with  50  cents  cash  in  hand.  For 
the  first  week,  you  receive  25 
cents  Monday,  and  spend  15  ;  30 
cents  Tuesday,  and  spend  18; 
and  so  on,  receiving  five  cents 
more  each  day,  and  spending 
three  cents  more  than  the  day 
before.  At  the  end  of  the  week 
you  will  have  $1.40.  The  sec- 
ond week,  your  receipts  and  ex- 
penditures are  equal  in  amount 
to  the  first,  but  reversed  as  to 
days  —  your  allowance  is  50 
cents  Monday,  and  you  spend 
30 ;  45  cents  Tuesday,  and  you 
spend  27 ;  and  so  on.  On  the 
second  Saturday  your  expense 
account  will  be  the  same  as  for 
the  first  Monday  — you  receive 
25  cents  and  spend  15  ;  but  your 

accumulated  wealth  will  then  be 

Cash  increases  till  Expenses  and  Income         „  _,          ,  .    ,  , 

are  Equal  #2.30. 

receive    25    cents    Monday,    20 

cents  Tuesday,  and  so  on,  but  through  the  week  you  spend  1 5  cents 
each  day.  For  two  weeks  your  income  has  steadily  been  falling  off, 
from  50  cents  daily  to  nothing ;  but  your  total  cash  in  hand  kept  on 
accumulating,  and  did  not  begin  to  decrease  until  the  middle  of  the 


$2.00 


.60 


•iv        dy 
$1.00  -  -  -/- 

.90 V-- 


The  Seasons   Geographically  159 

third  week,  and  on  the  third  Saturday  you  close  the  account  with  $2.15 
in  hand.  Cash  in  hand  at  the  beginning  is  the  temperature  about 
the  middle  of  May,  and  the  end  of  the  first  week  corresponds  to  the 
summer  solstice.  Income  is  the  amount  of  heat  received  from  the 
sun,  and  expenditure  is  the  amount  radiated  into  space.  Just  as  cash 
in  hand  went  on  accumulating  long  after  receipts  began  to  fall  off,  so 
the  average  daily  temperature  keeps  on  rising  for  more  than  a  month 
after  the  solstice,  when  the  amount  received  each  day  is  greatest.  The 
diagram  shows  the  entire  account  at  a  glance,  and  illustrates  at  the  same 
time  a  method  of  investigation  much  employed  in  astronomical  and  other 
researches,  called  the  graphical  method.  Its  advantages  in  presenting 
the  range  of  fluctuations  clearly  to  the  eye  are  obvious. 

The  Seasons  Geographically.  —  The  astronomical  division 
of  the  seasons  has  already  been  given  in  the  figure  on 
page  155.  It  is  as  follows:  — 

Spring,  from  the  vernal  equinox,  three  months. 
Summer,  from  the  summer  solstice,  three  months. 
Autumn,  from  the  autumnal  equinox,  three  months. 
Winter,  from  the  winter  solstice,  three  months. 

But  according  to  the  division  among  the  months  of  the 
year,  as  commonly  recognized  in  this  part  of  the  world, 
each  season  precedes  the  astronomical  division  by  nearly 
a  month,  and  is  as  follows  :  — 

Spring    =  March,  April,  May. 

Summer  =  June,  July,  August. 

Autumn  =  September,  October,  November. 

Winter    =  December,  January,  February. 

Differences  of  climate  and  in  the  forward  or  backward 
state  of  vegetable  life,  in  part  dependent  upon  local  condi- 
tions, have  led  to  different  divisions  of  the  calendar  months 
among  the  seasons,  varying  quite  independently  of  the 
latitude.  Great  Britain's  spring  begins  in  February,  its 
summer  in  May,  and  so  on.  Toward  the  equator  the 
difference  of  season  is  less  pronounced,  because  the  an- 
nual variation  of  the  sun's  meridian  altitude  is  less ;  and 
as  changes  in  rainfall  are  more  marked  than  those  of 


160        The  Earth  Revolves  Round  the  Sun 

temperature,  the  seasons  are  known  as  dry  and  rainy, 
rather  than  hot  and  cold.  These  marked  differences  of 
season  are  recognized  by  the  division  of  the  earth's  sur- 
face into  five  zones. 

Terrestrial  Zones.  —  From  the  relation  of  equator  to  eclip- 
tic, and  from  the  sun's  annual  motion,  it  is  plain  that  thrice 
every  year  the  sun  must  shine  vertically  over  every  place 
whose  latitude  is  less  than  23^°,  whether  north  or  south. 
This  geometric  relation  gives  rise  to  the  parallels  of  lati- 
tude called  the  tropics  ;  the  Tropic  of  Cancer  being  at  23  J° 
north  of  the  equator,  and  the  Tropic  of  Capricorn  at  23^° 
south.  They  receive  their  names  from  the  zodiacal  signs  in 
which  the  sun  appears  at  these  seasons.  The  belt  of  the 
earth  included  between  these  small  circles  of  the  terrestrial 
sphere  is  called  the  torrid  zone.  Its  width  is  47°,  or  nearly 
3300  miles.  Similarly  there  are  zones  around  the  earth's 
poles  where,  for  many  days  during  every  year,  the  sun 
will  neither  rise  nor  set.  These  polar  zones  or  caps  are 
also  47°  in  diameter.  Between  them  and  the  torrid  zone 
lie  the  two  temperate  zones,  one  in  the  northern  and  one 
in  the  southern  hemisphere,  each  43°,  or  about  3000  miles 
in  width.  The  sun  can  never  cross  the  zenith  of  any  place 
within  the  temperate  zones.  If  equator  and  ecliptic  were 
coincident,  that  is,  if  the  axis  of  the  earth  were  perpen- 
dicular to  the  plane  of  its  path  round  the  sun,  day  and 
night  would  never  vary  in  length,  and  our  present  division 
into  zones  would  vanish. 

The  Seasons  of  the  Southern  Hemisphere —  Our  earth 
in  traveling  round  the  sun  preserves  its  axis  not  only 
at  a  constant  angle  to  the  plane  of  its  orbit,  but  always 
for  a  limited  period  of  years  pointing  to  nearly  the  same 
part  of  the  heavens,  as  shown  in  the  figure  on  page  65. 
Plainly,  then,  the  seasons  of  the  southern  hemisphere  must 
occur  in  just  the  order  that  our  northern  seasons  do.  In 


Seasons  of  tJie  Southern  Hemisphere         161 

its  turn  the  south  pole  inclines  just  as  far  toward  the  sun 
as  the  north  one  does.  But  in  so  far  as  astronomical  con- 
ditions are  concerned,  the  southern  seasons  will  be  dis- 
placed just  six  months  of  the  calendar  year  from  ours. 
The  following  figures  of  the  earth  at  solstices  and  equi- 
noxes make  these  relations  clear.  Midwinter  in  the  south- 


Midsummer  in  the  Southern  Midsummer  in  the  Northern 

Hemisphere  Hemisphere 

ern  hemisphere  comes  in  June  and  July,  and  Christmas 
falls  in  midsummer.  The  opening  of  their  spring  comes 
in  August  and  September,  and  autumn  approaches  in 
February  and  March.  But  while  in  the  northern  hemi- 
sphere the  difference  between  the  heat  of  midsummer  and 
the  cold  of  midwinter  is  somewhat  lessened  by  the  chang- 
ing distance  of  the  sun,  in  the  southern  hemisphere  this 
effect  is  intensified,  because  the  earth  comes  to  perihelion 
in  the  southern  midsummer.  However,  on  account  of  the 
swifter  motion  of  the  earth  from  October  to  March  than 


Spring  in  the  Northern  Spring  in  the  Southern 

Hemisphere  Hemisphere 

from  April  to  September,  the  southern  summer  is  enough 
shorter  to  compensate  for  the  sun's  being  nearer,  so  that 
the  southern  summer  is  practically  no  hotter  than  the 
northern.  On  the  other  hand,  the  southern  winter  not 
only  lasts  about  seven  days  longer  than  the  northern,  but 

TODD'S    ASTRON.  —  I  I 


1 62        The  Earth  Revolves  Round  the  Sun 

it  is  colder  also,  because  the  sun  is  then  farthest  away. 
The  range  of  difference  in  the  heat  received  at  perihelion 
and  aphelion  is  about  T^  part  of  the  total  amount. 

Annual  Aberration.  —  In  looking  from  a  window  into  a 
quiet,  rainy  day,  the  drops  are  seen  to  fall  straight  down 


Aberration  of  the  Raindrop  is  Greater  as  the  Body  moves  Swifter 

earthward  from  the  sky.  But  if,  instead  of  watching  from 
shelter,  you  go  out  in  the  rain  and  run  swiftly  through  it, 
the  effect  is  as  if  the  drops  were  to  slant  in  oblique  lines 
against  the  face.  For  the  man  under  the  umbrella,  the 
leisurely  boy  with  rubber  coat  and  hat  on,  and  the  courier 
caught  in  the  rain,  how  different  the  direction  from  which 
the  drops  seem  to  come.  A  similar  but  even  more  exag- 
gerated effect  may  be  watchecl  in  a  railway  train  speeding 
through  a  quiet  snowstorm ;  it  seems  as  if  the  flakes  sped 
past  in  an  opposite  direction,  in  white  streaks  almost  hori- 


The  Constant  of  Aberration  163 

zontal, — the  result  of  swift  motion  of  the  train,  combined 
with  that  of  the  slowly  falling  snow.  This  appearance  is 
called  aberration,  and  in  reality  the  same  effect  is  produced 
by  the  progressive  motion  of  light.  Now  replace  the  mov- 
ing train  by  the  earth  traveling  in  its  orbit  round  the  sun, 
and  let  the  falling  raindrop  or  snowflake  represent  the 
progressive  motion  of  light ;  then  as  the  angle  between 
the  plumb-line  and  the  direction  from  which  rain  or  snow 
seems  to  come  is  the  aberration  of  the  descending  drop  or 
flake,  so  the  angle  between  the  true  position  of  the  sun 
and  the  point  which  its  light  seems  to  radiate  from  is  the 
annual  aberration  of  light.  It  is  usually  called  aberration 
simply,  and  was  discovered  by  Bradley  in  1727. 

The  Constant  of  Aberration.  —  Notice  two  things  :  (a)  that 
raindrop  and  snowflake  both  appear  to  come  from  points 
in  advance  of  their  true  direction ;  (£)  that  this  angle  of 
aberration  is  less  as  the  velocity  of  the  falling  drop  or  flake 
is  greater.  The  snowflake  falls  very  slowly  in  comparison 
with  the  speed  of  the  train,  so  the  angle  of  aberration  was 
observed  to  be  perhaps  80°  or  more  ;  but  where  the  velocity 
of  the  raindrop  was  nearly  the  same  as  the  speed  of  the 
train,  the  angle  of  aberration  was  only  45°.  Now  imagine 
the  velocity  of  the  drop  increased  enormously,  until  it  is 
10,000  times  greater  than  the  speed  of  the  train :  then  we 
have  almost  exactly  the  relation  which  holds  in  the  case  of 
the  moving  earth  and  the  velocity  of  a  wave  of  light.  In 
a  second  of  time  the  earth  travels  i8j  miles,  and  light 
186,300  miles.  But  we  found  that  any  object  which  fills 
an  angle  of  i"  is  at  a  distance  equal  to  206,000  times  its 
own  breadth  ;  so  that  the  angle  of  annual  aberration  of  the 
sun  must  be  the  same  as  that  filled  by  an  object  at  a  dis- 
tance of  only  10,000  times  its  own  breadth.  This  angle  is 
20". 5,  and  it  is  called  the  constant  of  aberration.  It  cor- 
responds to  the  mean  motion  of  the  earth  in  its  orbit.  At 


164        The  Earth  Revolves  Round  the  Sun 


aphelion,  where  this  motion  is  slowest,  the  sun's  aberration 
drops  to  2oJ"  ;  at  perihelion,  where  fastest,  it  rises  to  2o|". 
The  constant  of  aberration  has  been  determined  with  great 
accuracy  from  observations  of  the  stars ;  and  its  exact  cor- 
respondence with  the  motion  of  the  earth  may  be  regarded 
as  indisputable  proof  of  our  motion  round  the  sun. 

Aberration  of  the  Stars.  —  Aberration  is  by  no  means 
confined  to  the  sun ;  but  it  affects  the  apparent  position 
of  the  fixed  stars  as  well.  Observation  shows  that  every 
star  seems  to  describe  every  year  in  the  sky  a  small  ellipse. 
These  aberration  ellipses  traversed  by  the  stars  all  have 

equal  major  axes;  that 
is,  an  arc  of  41",  or 
double  the  constant  of 
aberration.  But  their 
minor  axes  vary  with 
the  latitude,  or  distance 
of  the  star  from  the 
ecliptic.  Try  to  con- 
ceive these  ellipses  in 
the  sky;  the  major 
axis  of  each  one  coin- 
cides with  the  parallel 
of  latitude  through  the 
star,  and  their  size  is 
such  that  they  are  just 

beyond  the  power  of  human  vision.  About  50  aberration 
ellipses  placed  end  to  end  with  their  major  axes  in  line  would 
reach  across  the  disk  of  the  moon.  For  a  star  at  the  pole  of 
the  ecliptic,  the  minor  axis  is  equal  to  the  major  axis ;  that 
is,  the  star's  aberration  ellipse  is  a  circle  41"  in  diameter. 
As  shown  in  the  illustration,  the  ellipses  grow  more  and 
more  flattened,  for  stars  nearer  and  nearer  the  ecliptic; 
and  when  the  star's  latitude  is  zero,  the  aberration  ellipse 


Aberration  Ellipses  of  the  Stars 


The  Calendar  165 

becomes  seemingly  a  straight  line,  but  actually  a  small  arc 
of  the  ecliptic  itself,  41"  in  length.  In  calculating  all 
accurate  observations  of  the  stars,  a  correction  must  be 
applied  for  the  difference  between  the  center  of  the  ellipse 
(the  star's  average  place),  and  its  position  in  the  ellipse  on 
the  day  of  the  year  when  the  observation  was  made.  .Every 
star  partakes  of  this  motion,  and  thus  proof  of  earth's  mo- 
tion round  the  sun  becomes  many  million  fold. 

The  Year.  — Just  as  there  are  two  different  kinds  of  day, 
so  also  there  are  two  different  kinds  of  year.  Both  are 
dependent  upon  the  motion  of  the  earth  round  the  sun, 
but  the  points  of  departure  and  return  are  not  the  same. 
Starting  from  a  given  star  and  returning  to  the  same  star 
again,  the  earth  has  consumed  a  period  of  time  equal  to 
365  d.  6  h.  9  m.  9  sec.  This  is  the  length  of  the  sidereal  year. 
But  suppose  the  earth  to  start  upon  its  easterly  tour  from 
the  vernal  equinox,  or  first  of  Aries:  while  the  year  is 
elapsing,  this  point  travels  westward  by  precession  of  the 
equinoxes,  so  that  the  earth  meets  it  in  20  m.  23  sec.  less 
than  the  time  required  for  a  complete  sidereal  revolution. 
This,  then,  is  the  tropical  year,  and  its  length  is  equal  to 
365  d.  5  h.  48  m.  46  sec.  It  is  the  ordinary  year,  and 
forms  the  basis  of  the  calendar.  Another  kind  of  year, 
strictly  of  no  use  for  calendar  purposes,  is  called  the 
anomalistic  year,  and  is  the  time  consumed  by  the  earth 
in  traveling  from  perihelion  round  to  perihelion  again. 
We  saw  that  the  line  of  apsides  moves  slowly  forward, 
at  such  a  rate  that  it  requires  108,000  years  to  complete 
an  entire  circuit  of  the  ecliptic.  The  anomalistic  year, 
therefore,  is  over  4^  minutes  longer  than  the  sidereal 
year,  its  true  length  being  365  d.  6  h.  13  m.  48  s. 

The  Calendar.  —  Two  calendars  are  in  use  at  the  present 
day  by  the  nations  of  the  world :  the  Julian  calendar  and 
the  Gregorian  calendar. 


1 66        The  Earth  Revolves  Round  the  Sun 


The  former  is  named  after  Julius  Caesar,  who,  in  B.C.  46,  reformed  the 
calendar  in  accordance  with  calculations  of  the  astronomer  Sosigenes. 
The  true  length  of  the  year  was  known  by  him  to  be  very  nearly  3651 
days  ;  so  Caesar  decreed  that  three  successive  years  of  365  days  should 
be  followed  by  a  year  of  366  days  perpetually.  But  as  the  Julian  year 
is  1 1. 2  minutes  too  long,  the  error  amounts  to  about  three  days  every 
400  years.  In  the  latter  part  of  the  i6th  century,  the  accumulation  of 
error  amounted  to  10  days.  Pope  Gregory  XIII  corrected  this,  and 
established  a  farther  reform,  whereby  three  leap-year  days  are  omitted 
in  four  centuries.  Years  completing  the  century,  as  1900  and  2000,  are 
cent nr ial  years .  Every  year  not  centurial  whose  number  is  exactly  divisi- 
ble by  4  is  a  leap  year ;  but  centurial  years  are  leap  years  only  when 
exactly  divisible  by  400.  The  year  1900,  then,  is  not  a  leap  year,  but 
the  year  2000  is.  In  1752  England  adopted  the  Gregorian  calendar,  and 
earlier  dates  are  usually  marked  o.  s.  (old  style).  At  the  same  time, 
England  transferred  the  beginning  of  the  year  from  25th  March  to  1st 
January,  the  date  adopted  by  Scotland  in  1600,  and  by  France  in  1563. 
Thus  before  1752,  dates  between  ist  January  and  24th  March  fell  in  dif- 
ferent years  in  England  and  in  Scotland  or  France,  and  frequently  both 
years  are  written  in  early  English  dates — as  23d  January,  I7'if,  the  lower 
figure  indicating  the  year  according  to  Scotch  and  French,  and  the 
upper  to  early  English,  reckoning.  Russia  and  Greece  still  employ  the 
Julian  calendar.  Dates  in  these  countries  are  usually  written  in  frac- 
tional form ;  for  example,  July  \\,  the  numerator  referring  to  the  Julian 
calendar,  and  the  denominator  to  the  Gregorian.  The  year  1900  is, 
therefore,  a  leap  year  in  Russia  and  Greece,  and  their  difference  of  reckon- 
ing from  ours  is  13  days  through  the  2oth  century. 

The  Week.  —  It  embraces  seven  days,  and  has  been 
recognized  from  the  remotest  antiquity.  Its  days  are  :  — 

THE  DAYS  OF  THE  WEEK 


ENGLISH 

SYMBOL 

DERIVATION 

FRENCH 

GERMAN 

Sunday 

O 

Sun's  day 

Dimanche 

Sontag 

Monday 

$ 

Moon's  day 

Lundi 

Montag 

Tuesday 

/ 

Tuisco's  day 

Mardi 

Dienstag 

Wednesday 

& 

Woden's  day 

Mercredi 

Mittwoch 

Thursday 

11 

Thor's  day 

Jeudi 

Donnerstag 

Friday 

9 

Freya's  day 

Vendredi 

Freitag 

Saturday 

k 

Saturn's  day 

Samedi 

Sonnabend 

Reforming  the  Calendar 


Tuisco  is  Saxon  for  the  deity  corresponding  to  the  Roman  Mars, 
Woden  for  Mercury,  Thor  for  Jupiter,  and  Freya  for  Venus-;  therefore 
the  symbols  of  the  corresponding  planets  were  adopted  as  designating 
the  appropriate  days  of  the  week.  These  symbols  are  more  often  used 
in  foreign  countries  than  in  our  own.  The  relation  of  the  week  to  the 
year  is  so  close  (52  xy  =  364)  as  to  suggest  a  possible  improvement  in 
the  calendar. 

Memorizing  the  Days  in  the  Month.  —  To  many  persons 
the  varying  number  of  days  in  the  months  of  our  year  is 
a  great  inconvenience.  This  time-worn  stanza  is  sometimes 

helpful :  - 

Thirty  days  hath  September, 

April,  June,  and  November ; 

All  the  rest  have  thirty-one, 

Save  February,  which  alone 

Hath  twenty-eight,  and  one  day  more 

We  add  to  it  one  year  in  four. 

The  facts  are  there,  even  if  the  rhythm  cannot  be  defended.  An 
easier  method  of  memorizing  the  succession  is  apparent  from  the  illus- 
tration below:  Close  the  hand  and  count  out  the  months  on  the 
knuckles  and  the  depressions  between  them,  until  July  is  reached,  then 
begin  over  again.  The  knuckles  represent  long  months,  and  the  de- 
pressions short  ones. 

Reforming  the  Calendar. — The  inconveniences  of  our  present  Gre- 
gorian calendar  are  many.  Some  authorities  think  it  on  the  whole  no 
improvement  on  the  Julian 
calendar ;  and  certainly  much 
confusion  would  have  been 
avoided,  if  the  Julian  cal- 
endar had  been  continued 
in  use  everywhere.  A  re- 
turn to  the  Julian  reckoning 
at  the  beginning  of  the  2oth 
century,  ist  January,  1901,  JUNE  j 

has  been  suggested  by  New- 
comb,    the    eminent    Amer- 
ican astronomer  ;    but  such   a        To  recall  the  Number  of  Days  in  Each  Month 
change     could    be     brought 

about  only  by  wide  international  agreement.  An  obvious  change  hav- 
ing many  advantages  would  be  the  division  of  the  year  into  13  months, 
each  month  having  invariably  28  days,  or  exactly  four  weeks.  Legal 
holidays  and  anniversaries  would  then  recur  on  the  same  days  of  the 


JANUARY  •< 

AUGUST  / 

FEBRUARY  '\ 

SEPTEMBER) 

MARCH  1 

OCTOBER  r 


MAY  i 

DECEMBER    / 


1 68        The  Earth  Revolves  Round  the  Sun 


week  perpetually.  The  chief  difficulty  would  arise  in  the  proper  dispo- 
sition of  the  extra  day  at  the  end  of  each  ordinary  year ;  and  of  two 
extra  days  at  the  end  of  each  leap  year. 

Easter  Sunday.  —  Easter  Day  is  a  movable  festival,  because  it  falls 
on  different  days  in  different  years.  By  decree  of  the  Council  of 
Nicaea,  A.D.  325,  Easter  is  kept  on  the  Sunday  which  falls  next  after 
the  first  full  moon  following  the  2 1st  of  March.  If  a  full  moon  falls 
on  that  day,  then  the  next  full  moon  is  the  Paschal  moon ;  and  if  the 
Paschal  moon  itself  falls  on  Sunday,  then  the  next  following  Sunday 
is  Easter  Day.  Many  have  been  the  bitter  controversies  about  the 
proper  Sunday  to  be  observed  as  Easter  Day,  in  years  when  the  rule 
was  from  the  nature  of  the  case  ambiguous.  Easter  Day  is  not,  how- 
ever, determined  by  the  true  sun  and  moon,  but  by  the  motion  of  the 
fictitious  sun  and  of  a  fictitious  moon  imagined  to  travel  uniformly  with 
the  time,  and  to  go  once  round  the  celestial  equator,  in  exactly  the 
same  time  that  the  real  bodies  travel  once  round  the  heavens.  Conse- 
quently the  above  rule  must  frequently  fail,  if  applied  to  the  phases  of 
the  moon  as  given  in  the  almanac.  Following  are  the  dates  of  Easter 
for  about  a  quarter  century  :  — 

EASTER  DAY,  1890-1913 


YEAR 

DATE 

YEAR 

DATE 

YEAR 

DATE 

YEAR 

DATE 

1890 

April      6 

l896 

April    5 

1902 

March  30 

1908 

April     19 

1891 

March  29 

1897 

April  1  8 

1903 

April     1  2 

1909 

April     1  1 

1892 

April     17 

1898 

April  10 

1904 

April      3 

1910 

March  27 

1893 

April      2 

I899 

April    2 

1905 

April    23 

1911 

April     1  6 

1894 

March  25 

1900 

April  15 

1906 

April     1  5 

1912 

April       7 

I895 

April     14 

1901 

April    7 

1907 

March  31 

I9U 

March  23 

Having  now  learned  the  A  B  C's  of  the  language  which 
astronomers  use,  and  having  studied  the  earth  as  a  revolv- 
ing globe  and  the  seeming  motions  of  the  stars  relatively 
to  it ;  also  having  ascertained  many  facts  connected  with 
our  yearly  journey  round  the  sun,  —  we  may  next  seek 
to  apply  that  knowledge  in  a  long  voyage>  begun  early 
in  December,  from  New  York  to  Yokohama  by  way  of 
Cape  Horn. 


CHAPTER   VIII 

THE  ASTRONOMY  OF  NAVIGATION 

ON  an  actual  voyage  to  Japan  and  back,  we  shall  in- 
vestigate new  astronomical  questions  in  the  order 
of  their  coming  to  our  notice,   and  verify   many 
astronomical  relations    founded   on   geometric    truth.     So 
we  shall  be  learning  a  cosmopolitan  astronomy  of  use  in 
foreign  countries  as  well  as  at  home,  and  acquiring  some 
knowledge  of  astronomical  methods  by  which  ships  are 
safely  guided  across  the  oceans. 

Navigation.  — Navigation  is  the  art  of  conducting  a  ship 
safely  from  one  port  to  another.  When  a  ship  has  gone 
20  miles  out  to  sea,  all  landmarks  will  usually  have  disap- 
peared, and  the  sea  horizon  will  extend  all  the  way  round 
the  sky.  Look  in  whatsoever  direction  we  will,  nothing 
can  be  seen  but  an  expanse  of  water  (page  25),  appar- 
ently boundless  in  extent.  Outside  the  ship  there  is 
nothing  whatever  to  tell  us  where  we  are,  or  in  what 
direction  to  steer  our  craft.  Every  direction  looks  like 
every  other  direction.  Still  the  accurate  position  of  the 
ship  must  be  found.  The  only  resource,  then,  is  to 
observe  the  heavenly  bodies,  and  their  relation  to  the 
horizon. 

The  navigator  must  previously  have  provided  himself  with  the  lesser 
instruments  necessary  for  such  observation  ;  and  the  technical  books 
and  mathematical  tables  by  means  of  which  his  observations  are  to  be 
calculated.  These  processes  of  navigation  are  astronomical  in  charac- 
ter, and  the  principles  involved  are  employed  on  board  every  ship. 

169. 


170 


The  Astronomy  of  Navigation 


The  computations  required  in  ordinary  navigation  are  based  upon  the 
data  of  an  astronomical  book  called  the  Nautical  Almanac. 

The  Nautical  Almanac.  —  The  Nautical  Almanac  contains  the  accu- 
rate positions  of  the  heavenly  bodies.  They  are  calculated  three  or 
four  years  in  advance,  and  published  by  the  leading  nations  of  the 
globe.  Foremost  are  the  British,  American,  German,  and  French  Nau- 
tical Almanacs.  Below  is  a  part  of  a  page  of  The  American  Ephemeris 
and  Nautical  Almanac  for  1899,  showing  data  relating  to  the  sun. 

OCTOBER,  1899 


AT  GREENWICH  APPARENT  NOON 


1 

II 

,15 

C 
O 

THE  SUN'S 

Sidereal 
Time  of 
Semi- 

Equation 
of  Time, 
to  be 

i 

'S 

,C 

^ 

diam- 

Subtracted 

M 

I 

rt 

Apparent 
Right 
Ascension 

.*! 

Apparent 
Declination 

for' 

i 

Semi- 
diameter 

eter 
Passing 
Merid- 

from 
Apparent 
Time 

| 

Q 

Q 

Q      M 

Hour 

ian 

Q 

h.     m.    s. 

s. 

0            '        H 

« 

.     » 

s. 

m.      s. 

s. 

SUN. 

1 

122939.39 

9.058 

s.  31215-5 

-58.27 

161.37 

64-37 

10  19.23 

0.796 

Mon. 

2 

1233  16.94 

9.071 

3  35  33-o 

58.18 

16  1.64 

6441 

1038.18 

0.783 

Tues. 

3 

12  36  54-82 

9.085 

3  5848.0 

58.07 

16  1.91 

64.46 

10  56.81 

0.769 

Wed. 

4 

124033.03 

9.099 

422   0.3 

—57-95 

16  2.19 

64.51 

II  I5.IO 

0-755 

Thur. 

5 

1244  11.59 

9.114 

445    9-4 

57-8i 

162.47 

64.56 

II  3304 

0.740 

Frid. 

6 

124750.52 

9.130 

5    8  '4-9 

57-65 

162.75 

64.62 

II  50.61 

0.724 

Sat. 

7 

1251  29.84 

9.147 

53i  16-5 

-57-48 

163.03 

64.68 

12     7.80 

0.708 

SUN. 

8 

1255     9-56 

9.164 

5  54  13-8 

57-29 

163-31 

64.74 

1224.59 

0.691 

Mon. 

9 

125849.70 

9.182 

617    6.4 

57-09 

16  3.60 

64.80 

12  40.96 

0.673 

The  intervals  here  are  one  day  apart ;  but  for  the  moon,  which  moves 
among  the  stars  much  more  rapidly,  the  position  is  given  for  every  hour. 
Also  the  angular  distance  of  the  moon  from  certain  stars  and  planets  is 
given  at  intervals  of  three  hours.  Upon  the  precision  of  the  Nautical 
Almanac  depends  the  safety  of  all  the  ships  on  the  oceans.  Besides 
the  figures  required  in  navigating  ships,  the  Nautical  Almanacs  contain 
a  great  variety  of  other  data  concerning  the  heavenly  bodies,  used  by 
surveyors  in  the  field  and  by  astronomers  in  observatories. 

The  Ship's  Chronometers.  —  Some  hours  before  the  departure  of  the 
vessel,  two  boxes  about  a  foot  square  are  brought  on  board  with  the 
greatest  care,  and  secured  in  the  safest  part  of  the  ship,  where  the  tem- 
perature will  be  nearly  constant.  Within  each  box  is  another,  about 
eight  inches  square,  shown  open  in  the  picture  opposite.  Inside  it  is  a 
large  watch,  very  accurately  made  and  adjusted,  forming  one  of  the 
most  important  instruments  used  in  conducting  ships  from  port  to  port. 


Chronometers 


171 


It  is  called  the  marine  chronometer,  or  box  chronometer,  but  generally 
the  chronometer  simply.  The  face,  about  4!-  inches  in  diameter,  is 
usually  dialed  to  12  hours,  as  in  ordinary  watches.  In  addition  to  the 
second  hand  at  the  bottom  of  the  face,  there  is  a  separate  index  at  the 
top  to  indicate  how  many  hours  the  chronometer  has  been  running 
since  last  wound  up ;  for,  like  all  good  watches,  winding  at  the  same 
hour  every  day  is  essential. 
Spring  and  gears  are  so  re- 
lated that  a  chronometer 
ordinarily  runs  56  hours, 
though  it  should  be  wound 
with  great  care  at  regular 
intervals  of  24  hours — the 
extra  32  being  a  concession 
to  possible  lapses  of  mem- 
ory. Other  chronometers, 
wound  regularly  every  week, 
are  constructed  to  run  an 
extra  day,  and  so  are  called 
1  eight-day'  chronometers. 
All  these  instruments  are  so 
jeweled  that  they  will  run 
perfectly  only  when  the  face 
is  kept  horizontal ;  they  are 
therefore  hung  in  gimbals,  a 
device  with  an  intermediate 
ring,  and  two  sets  of  bearings 
with  axes  perpendicular  to 
each  other.  As  the  chro- 
nometer case  is  hung  far  above  its  center  of  gravity,  its  face  always 
remains  horizontal,  no  matter  what  may  be  the  tilt  of  the  outer  box, 
in  consequence  of  the  rolling  or  pitching  of  the  ship.  The  instrument 
shown  in  the  illustration  is  of  that  particular  type  known  as  a  break- 
circuit  chronometer,  so  called  because  an  electric  circuit  (through  wires 
attached  to  the  two  binding  posts  on  the  left  side  of  the  box)  is  auto- 
matically broken  at  the  beginning  of  every  second,  by  means  of  a  very 
delicate  spring  attached  alongside  one  of  the  arbors.  Such  a  chronom- 
eter is  generally  employed  by  surveying  expeditions  in  the  field,  where 
a  chronograph  (page  213)  is  needed  to  record  the  star  observations, 
and  where  a  clock  would  be  too  bulky  and  inconvenient. 

What  the  Chronometers  are  for.  —  The  real  purpose  of  chronometers 
is  to  carry  Greenwich  time,  and  the  need  of  this  is  made  clear  farther 
on.  For  at  least  a  fortnight  before  they  are  brought  on  board  ship,  all 
chronometers  are  carefully  tested  and  compared  with  a  standard  clock, 


The  Chronometer 


172 


The  Astronomy  of  Navigation 


regulated  by  frequent  observations  of  the  sun  and  stars,  usually  at 
some  astronomical  observatory.  So  at  the  outset  of  our  voyage  we 
see  how  intimate  is  the  relation  between  practical  astronomy  and  the 
useful  art  of  navigation.  The  navigator  of  the  ship  is  provided  with  a 
memorandum  for  each  chronometer,  showing  how  much  it  is  fast  or 
slow  on  Greenwich  time,  and  how  much  it  is  gaining  or  losing  daily. 
The  amount  by  which  it  is  fast  or  slow  is  called  the  chronometer  error 
or  correction ;  and  the  rate  is  the  amount  it  gains  or  loses  in  24  hours. 
If  the  chronometer  is  a  good  one  and  well  adjusted,  the  rate  should  be 
only  a  small  fraction  of  a  second.  As  a  rule,  on  voyages  of  moderate 
length,  the  Greenwich  time  can  always  be  found  from  the  chronometers 
within  three  or  four  seconds  of  the  truth.  This  uncertainty  amounts 
to  about  a  mile  in  the  position  of  the  ship.  To  avoid  the  possibility  of 
entire  loss  of  the  Greenwich  time  by  any  accident  to  a  single  chronom- 
eter, ships  nearly  always  carry  two,  and  often  many  more. 

The  Works  of  the  Chronometer.  —  Familiarity  with  the  interior  of  any 
watch  will  help  in  understanding  the  finer  and  more  complicated  works 


Works  of  the  Chronometer  (Size  compared  with  Ordinary  Watch) 

of  the  chronometer,  well  shown  in  the  illustration.  The  ordinary  watcb 
alongside  indicates  the  relative  size  of  the  parts.  The  chronometer 
balance  is  about  one  inch  in  diameter,  and  the  hairspring  about  \  inch 
in  diameter,  and  \  inch  high.  Fusee,  winding  post,  and  some  other  de- 
tails are  well  seen.  On  the  left  is  the  glass  crystal,  set  in  a  brass  cell 
which  screws  on  top  of  the  brass  case,  shown  on  the  right.  On  the 
right-hand  side  of  this  case  is  seen  one  of  the  pivot  bearings  by  which 
it  swings  in  the  gimbals. 

The  Chronometer  Balance.  —  A  balance  compensated  for  temperature 
is  necessary  to  the  satisfactory  running  of  a  chronometer,  because  a 
chronometer  with  a  plain,  uncompensated  brass  balance  will  lose  6\ 
seconds  daily  for  each  Fahrenheit  degree  of  rise  in  temperature.  In 


Time  on  Board  Ship 


173 


order  to  counteract  this  effect,  marine  chronometers  (and  all  good 
watches)  are  provided  with  a  balance,  the  principle  of  which  is  shown 
in  the  illustration.  The  arm  passing  centrally  through  the  balance  is 
of  steel,  and  at  its  ends  are  two  large-headed  screws,  for  making  the 
chronometer  run  correctly  at  a 
standard  temperature,  say  62°. 
The  semicircular  halves  of  the 
rim  are  cut  free,  being  attached 
to  the  arm  at  one  end  only. 
The  rim  itself  is  composed  of 
strips  of  brass  and  steel  firmly 
brazed  together.  The  outer 
part  is  brass,  and  the  inner 
steel,  of  one  half  the  thickness  of 
the  brass.  With  a  rise  of  tem- 
perature, brass  tends  to  expand 
more  rapidly  than  steel ;  and 
by  overpowering  the  steel,  it 
bends  the  free  ends  of  the  rim 
inward,  practically  making  the 
balance  a  little  smaller.  When 
the  temperature  falls,  the  balance 

enlarges  again  slightly.  Near  the  middle  of  each  half  rim  is  a  weight, 
which  can  be  moved  along  the  rim.  Delicate  adjustment  for  heat  and 
cold  is  effected  by  trial,  the  chronometer  being  subjected  to  varying 
temperatures  in  carefully  regulated  ovens  and  refrigerating  boxes.  The 
weights  are  moved  along  the  rim  until  gain  or  loss  is  least,  no  matter 
what  the  thermometer  may  indicate. 

Time  on  Board  Ship.  —  The  time  for  everybody  on  board  ship  is 
regulated  according  to  an  arbitrary  division  adopted  by  navigators. 
The  day  of  24  hours  is  subdivided  into  six  periods  of  four  hours  each, 
called  watches.  A  watch  is  a  convenient  interval  of  duty  for  both 
officers  and  sailors ;  and  this  division  of  the  ship's  day  is  recognized 
by  mariners  the  world  over.  The  period  from  4  P.M.  to  8  P.M.  is  sub- 
divided into  two  equal  parts,  called  dogwatches  ;  so  that  the  seven 
watches  of  the  ship's  day,  with  their  names,  are  as  follows  :  — 


The  Chronometer  Balance 


The  first  watch, 
The  mid  watch, 
The  morning  watch. 
The  forenoon  watch, 
The  afternoon  watch. 
The  first  dogwatch, 


from    8  P.M.  to  12  midnight, 

from  12  midnight  to    4  A.M. 
from    4  A.M.          to    8  A.M. 
from    8  A.M.          to  12  noon, 
from  12  noon          to    4P.M. 
from    4  P.M.          to    6  P.M. 


The  second  dogwatch,  from    6  P.M.          to    8  P.M. 


1 74  The  Astronomy  of  Navigation 

The  dogwatches  differ  in  length  from  the  regular  watches,  so  that 
during  the  cruise  the  hours  of  duty  for  officers  and  men  may  be  dis- 
tributed impartially  through  day  and  night.  Every  watch  of  four  hours 
is  again  divided  into  eight  periods,  each  a  half  hour  long,  called  bells. 
Each  watch,  except  the  dogwatches,  therefore,  continues  through  eight 
bells.  The  end  of  the  first  half-hour  period  of  each  watch  is  called  one 
bell;  of  the  second,  two  bells;  of  the  third,  three  bells;  and  so  on. 
Four  bells,  for  example,  corresponds  to  two  o'clock,  six  o'clock,  and  ten 
o'clock ;  and  seven  bells  to  half  past  three,  half  past  seven,  and  half 
past  eleven,  whether  A.M.  or  P.M.,  of  time  on  shore. 

Low  Tide  delays  the  Ship's  Departure.  —  Another  point  of 
contact  between  astronomy  and  navigation  was  well  illus- 
trated as  the  ship  was  about  to  depart.  The  tide  was  low, 
and  she  must  wait  a  few  hours  until  it  rose.  The  times  of 
high  tide  and  low  tide  are  predicted  by  calculations  based 
in  large  part  upon  the  labors  of  astronomers.  The  mere 
phenomena  of  tides  are  inquired  into  here,  leaving  the 
explanation  of  them  to  a  subsequent  chapter  on  universal 
gravitation. 

The  Tides  in  General.  —  A  visit  of  one  day  to  the  seashore 
is  sufficient  to  show  the  rising  and  falling  of  the  ocean.  It 
may  happen  that  in  the  morning  a  walk  can  be  taken 
along  the  broad,  sandy  beach,  which  later  in  the  day  will  be 
covered  under  the  risen  waves.  Or  rocks  where  one  sat  in 
the  morning  are  in  the  afternoon  buried  underneath  green 
water.  A  single  day  will  always  show  these  changes  ;  and 
another  single  day  will  exhibit  similar  fluctuations,  only  at 
other  hours.  The  photographic  picture  opposite  indicates 
a  typical  range  of  the  tides,  and  horizontal  markings  on 
the  rocks  show  the  level  of  high  tide,  seven  or  eight  feet 
above  water  level  in  the  illustration.  A  week's  stay  at  the 
shore  will  establish  the  regularity  of  variation.  High  tide 
at  ten  o'clock  in  the  morning  means  low  tide  a  little  after 
four  in  the  afternoon,  or  approximately  six  hours  later, 
high  tide  occurs  again  soon  after  ten  in  the  evening,  and 
low  tide  at  about  half  past  four  in  the  morning.  So  there 


The   Tides  Defined 


175 


are  two  high  tides  and  two  low  ones  in  every  24  hours,  or 
more  properly,  in  nearly  25  hours.  And  if  it  is  high  tide 
one  morning  at  ten  o'clock,  the  next  day  full  tide  will  occur 
at  about  eleven  o'clock.  So  that  gradually  the  times  of 
high  and  low  tide  change  through  the  whole  24  hours,  lag- 
ging about  50  minutes  from  one  day  to  another. 


At  Low  Tide  —  (Markings  on  Rocks  are  Level  of  High  Tide) 

The  Tides  defined.  —  A  tide  is  any  bodily  movement  of 
the  waters  of  the  earth  occasioned  by  the  attraction  of 
moon  and  sun.  The  word  tide,  as  used  by  the  sailor, 
often  refers  to  the  nearly  horizontal  flow  of  the  sea,  forth 
and  back,  in  channels  and  harbors.  To  the  astronomer, 
the  word  tide  means  a  vertical  rise  and  fall  of  the  waters, 
very  different  in  different  parts  of  the  earth,  due  to  the 
westerly  progress  of  the  tidal  wave  round  the  globe.  The 
time  of  highest  water  is  called  high  tide ;  and  of  lowest 
water,  low  tide.  From  high  tide  to  low  is  termed  ebb  tide  ; 
from  low  to  high,  flood  tide.  Near  new  moon  and  full 
moon  each  month  (as  explained  on  page  388)  occur  the 
highest  and  lowest  tides,  termed  spring  tides.  As  the 
moon  comes  to  new  and  full  every  month,  or  lunation,  and 
as  there  are  about  I2|  lunations  in  the  year,  there  are 
nearly  25  periods  of  spring  tides  annually.  Spring  tides 


176 


The  Astronomy  of  Navigation 


have  nothing  to  do  with  the  season  of  spring.  Intermedi- 
ate and  near  the  moon's  first  and  third  quarters,  the  ebb 
and  flood,  being  below  the  average,  are  called  neap  tides 
(flipped,  or  restricted  tides).  So  valuable  to  the  navigator 
is  a  knowledge  of  the  times  of  high  tide  and  low  tide 
at  all  important  ports,  that  these  times  are  carefully  calcu- 
lated and  published  by  government  authority  a  year  or 
two  in  advance.  This  duty  in  our  country  is  fulfilled  by 
the  United  States  Coast  and  Geodetic  Survey,  a  bureau  of 
the  Treasury  Department. 

Direct  and   Opposite  Tides.  —  The  tide  formed   on   the 
earth  as  a  whole  is  made  up  of  two  parts :  (a)  the  direct 
lum/to,       tide,  which  is  the  bulge  or  protuberance,  or  tidal 
/     s      |    wave  on  the  side  of  the  earth  toward  the  tide- 
raising  body,  and  (U]  the  opposite  tide,  which  is 
the  tidal  wave  on  the  side  away  from  it.     The 
figure  shows  a  section  of  the  earth  surrounded 
as  it  always  is  by  such  a  double  tide.     Gravita- 
tion, as  explained  in  the  chapter  on  that  subject, 
elongates  the  watery  envelope  of  the  earth  very 
slightly  in  two  opposite  directions.      Thus  the 
earth  and  its  waters  are  a  prolate  spheroid ;  that 
is,  slightly  football-shaped.     As  the  earth  turns 
round  on   its  axis  eastward,  this  watery  bulge 
seems  to  travel  from  east  to  west,  in  the  form 
of  a  tidal  wave  twice  every  25  hours.     To  illus- 
trate :  It  is  as  if  a  large  cannon  ball  were  turn- 
mg  on  tne  shorter  axis  of  a  football  and  inside 
opposite  Tides  of  jt     jf  tne  waters  could  at  once  respond  to 
the  moon's  attraction,  the  time  of  high  tide  would  coincide 
with  the   moon's   crossing   the  upper  or  lower  meridian. 
But  on  account  of  inertia  of  the  water,  the  comparatively 
feeble  tide-producing  force   requires  a  long  time  to  start 
the  wave.     The  time  between  moon's  meridian  transit  and 


© 


Movement  of  the   Tidal  Wave  1 7  7 

arrival  of  the  crest  of  the  tidal  wave  is  called  the  establish- 
ment of  the  port.  This  is  practically  a  constant  quantity 
for  any  particular  port,  but  is  different  for  different  ports. 
It  is  8J  hours  for  the  port  of  New  York. 

Only  the  Wave  Form  travels.  —  Guard  against  thinking  that  the 
tides  are  produced  by  the  waters  of  the  ocean  traveling  bodily  round 
the  globe  from  one  region  to  another.  The  deep  waters  merely  rise 
and  fall,  their  advance  movement  being  very  slight,  except  where  the 
tidal  wave  impinges  upon  coasts.  It  is  only  the  form  of  the  wave  that 
advances  westerly.  Illustrate  by  extending  a  piece  of  rope  on  the  floor 
and  shaking  one  end  of  it.  A  wave  runs  along  the  rope  from  one  end 
to  the  other ;  but  only  the  wave  form  advances,  the  particles  of  the 
rope  simply  rising  and  falling  in  their  turn.  So  with  the  waters  of 
the  tidal  wave. 

Movement  of  the  Tidal  Wave.  —  Originating  in  the  deep 
waters  of  the  Pacific  Ocean,  off  the  west  coast  of  South 
America,  the  tidal  wave  travels  westerly  at  speeds  varying 
with  the  depth  of  the  ocean.  The  deeper  the  ocean,  the 
faster  it  travels.  During  this  progressive  motion  of  a 
given  tidal  wave  it  combines  with  other  and  similar  tidal 
waves,  so^hat  the  resultant  is  always  complex.  In  about 
12  hours  it  reaches  New  Zealand,  passes  the  Cape  of 
Good  Hope  in  30  hours,  where  it  unites  with  (a)  the 
direct  tide  in  the  Atlantic  off  Africa,  and  (b)  a  reversed 
wave,  which  has  moved  easterly  round  Cape  Horn  into 
the  Atlantic.  The  united  wave  then  travels  northwesterly 
through  the  Atlantic  Ocean  about  700  miles  hourly,  reach 
ing  the  east  coast  of  the  United  States  in  40  hours.  On 
account  of  the  irregular  contour  of  ocean  beds,  there  is 
never  a  steadily  advancing  tidal  wave,  as  there  would 
be  if  the  oceans  covered  the  entire  earth  to  a  uniform 
depth.  Tidal  charts  of  the  oceans  have  drawn  upon  them 
irregularly  curved  lines  connecting  places  where  crests  of 
tidal  waves  arrive  at  the  same  hour  of  Greenwich  time. 
These  are  called  cotidal  lines. 
TODD'S  ASTRON. —  12 


178  The  Astronomy  of  Navigation 

Extent  of  Rise  and  Fall.  — The  extent  of  rise  and  fall  of  the  tide 
varies  in  different  places.  Speaking  generally,  in  mid-ocean  the  differ- 
ence between  high  and  low  water  is  between  two  and  three  feet,  while 
on  the  shores  of  great  continents,  especially  in  shallow  and  gradually 
narrowing  bays,  the  height  is  often  very  great.  The  average  spring 
tide  at  New  York  is  about  5}  feet,  and  at  Boston  about  u.  In  the 
Bay  of  Fundy,  spring  tides  rise  often  60  feet,  and  sometimes  more. 
The  tide  also  rises  in  rivers,  but  less  as  the  distance  from  the  river's 
mouth  increases,  where  it  is  more  and  more  neutralized  by  the  current. 
A  tide  of  a  few  inches  advances  up  the  Hudson  River  from  New  York 
to  Albany  in  about  nine  hours.  It  is  possible  for  a  river  tide  to  rise  to 
a  higher  level  than  that  of  the  ocean  itself,  where  the  momentum  of  the 
wave  is  expended  -in  raising  a  relatively  small  amount  of  water,  on 
the  principle  of  the  hydraulic  ram.  At  Batsha  in  Tonquin  there  is  no 
tide  whatever,  because  the  waters  enter  by  two  mouths  or  channels 
of  unequal  depth  and  length,  the  .lagging  in  the  longer  channel  being 
about  six  hours  more  than  in  the  shorter  one. 

Tides  in  the  Great  Lakes.  —  Theoretically  there  are  tides  in  large 
bodies  of  inland  water  also ;  but  even  the  largest  lakes  are  too  small 
for  their  share  in  the  moon's  tide-producing  force  to  be  very  pronounced. 
A  tide  of  less  than  two  inches  occurs  in  Lake  Michigan  at  Chicago ; 
and  in  the  Mediterranean  there  is  a  slight  tide  of  about  18  inches. 
Height  of  the  tide  in  landlocked  seas  depends  in  part  upon  the  ratio 
of  the  length  of  such  seas  (east  and  west)  to  the  diameter  of  the  earth. 
Meager  tides  like  these  are  often  completely  masked  by  the  tides  which 
local  winds  raise. 

Duration  of  Flood  and  Ebb  Tides.  —  In  mid-ocean  the 
tidal  wave  rises  much  less  than  on  the  coasts ;  for  on 


Direction   of  advance   of  tidal   wave 
Ebb  Tide  always  longer  than  Flood  Tide 

reaching  shallow  water,  friction  retards  the  wave,  shorten- 
ing its  length  from  crest  to  crest,  and  greatly  increasing 
the  height  of  the  tide,  particularly  if  the  advancing  wave 
is  forced  to  ascend  a  sc  aewhat  shallow  and  gradually 
narrowing  channel. 

Above  figure  illustrates  this  change  in  the  section  of  a  tidal  wave 
advancing  toward  a  coast  on  the  right.    The  crest  of  the  wave  is  farther 


Diurnal  Inequality  of  the    Tides  179 

from  the  bottom  and  therefore  less  retarded  by  friction,  so  that  it 
advances  more  rapidly,  and  makes  the  wave  steeper  on  its  front  than 
on  its  after  slope.  Under  all  ordinary  conditions,  then,  flood  tide  is 
evidently  shorter  in  duration  than  ebb  tide.  At  Philadelphia,  for 
example,  where  the  difference  is  accentuated  by  coast  configurations 
ebb  tide  is  nearly  two  hours  longer  than  flood  tide.  An  extreme  case 
is  that  known  as  the  tidal  bore,  in  which  the  advancing  slope  of  the 
tidal  wave  in  certain  favorably  conditioned  rivers  becomes  perpendicular. 


Tidal  Bore  at  Caudebec,  a  town  on  the  Seine  (according  to  Flammarion) 

The  crest  then  topples  over,  and  flood  tide  takes  the  form  of  a  swiftly 
advancing  breaker ;  in  only  a  few  minutes  the  waters  rise  from  low  to 
high,  and  ebb  tide  consumes  rather  more  than  12  hours  following.  This 
strong  tidal  wave  surmounting  the  seaward  current  of  the  river,  some- 
times piling  up  a  cascade  of  overlapping  waves,  is  well  marked  in  the 
Seine,  the  Severn,  and  the  Ganges. 

'lO 

Diurnal  Inequality  of  the  Tides.  —  If  the  earth's  equator 
coincided  with  the  plane  of  the  moon's  orbit,  and  if  there 
were  no  obliquity  of  the  ecliptic,  evidently  the  tide-produc- 


i8o 


The  Astronomy  of  Navigation 


ing  force  of  both  sun  and  moon  would  always  act  perpen- 
dicular to  the  earth's  axis.  The  direct  tide  and  the  opposite 
tide  would  then  be  symmetrical  with  reference  to  the 
equator;  and,  generally  speaking,  equal  latitudes  would 
experience  equal  tides.  When,  however,  the  moon  is  at  her 


s  f 


MOON    FARTHEST 
SOUTH  OF  EQUATOR 

S  S     I      M 


SAN     FRANC 


fa/   lines   twp  feet  \  apart 


Diurnal  Inequality  of  the  Tides  at  San  Francisco 

greatest  declination  north,  the  direct  tide  is  highest  at  those 
north  latitudes  where  the  moon  culminates  at  the  zenith ; 
while  the  opposite  tide  is  slight  in  the  northern  hemi- 
sphere, but  highest  at  the  antipodes  of  the  direct  tide,  or 
in  south  latitudes  equal  to  the  north  declination  of  the 
moon.  This  difference  in  height  of  the  two  daily  tidal 
waves  is  called  the  diurnal  inequality. 

In  the  case  of  lunar  tidal  waves,  the  diurnal  inequality  becomes 
zero  twice  each  month,  when  the  moon  crosses  the  celestial  equator; 
and  the  diurnal  inequality  of  the  solar  tide  vanishes  at  the  equinoxes. 
But  this  obvious  difference  in  height  of  the  two  daily  tides  is  greatly 
modified  by  coast  configurations  and  other  conditions.  The  illustration 
above  is  plotted  from  a  fortnight's  record  of  the  tide  gauge  at  San 
Francisco.  The  wave  line  represents  the  rise  and  fall  of  the  surface 
of  the  water;  the  distance  from  one  horizontal  line  to  another  being 
two  feet.  Vertical  lines  divide  off  periods  of  24  hours,  the  succession 
of  days  being  indicated  at  the  top.  The  difference  between  direct  and 
opposite  tide  is  very  marked  each  day,  except  when  the  moon  is  near 
the  equator,  when  the  diurnal  inequality  is  much  reduced.  Small  dots 
are  placed  adjacent  to  the  highs  and  lows  of  the  direct  tide,  which 
illustrate  the  diurnal  inequality  excellently,  having  a  very  wide  range 
in  northern  latitudes  when  the  moon  culminates  nearest  the  zenith,  a 
medium  range  when  she  is  crossing  the  equator,  and  a  minimum  range 
when  her  south  declination  is  near  a  maximum. 


The  Sextant 


181 


The  Sextant.  —  The  sextant  is  a  light,  portable  instru- 
ment arranged  for  measuring  conveniently  arcs  of  a  great 
circle  of  the  celestial  sphere  in  any  plane  whatever.  With 
it  are  made  the  astronomi- 
cal observations  which  are 
calculated  by  means  of  the 
Nautical  Almanac.  Next 
to  the  compass,  the  sex- 
tant is  more  frequently 
used  than  any  other  in- 
strument; for  by  the 
angles  measured  with  it, 
the  navigator  finds  his 
position  upon  the  ocean 

from    day    tO    day.  Sextant  for  measuring  Angles 

In  navigation  the  sextant  is  generally  used  in  a  vertical  plane ;  that 
is,  in  measuring  altitudes  of  heavenly  bodies.  The  sextant  was  in- 
vented by  Hadley  in  1730.  A  finely  graduated  arc  A,  of  60°  (whence 
the  origin  of  its  name)  has  an  arm  (from  /downward  toward  the  right) 
sliding  along  it,  as  the  radius  of  a  circle  would,  if  pivoted  at  the  center 
and  moved  round  the  circumference.  Rigidly  attached  to  the  pivot 
end  of  this  moving  arm,  and  at  right  angles  to  the  plane  of  the  arc,  is 
a  mirror,  /,  called  the  index  glass.  Also  firmly  attached  to  the  frame 
of  the  arc  is  another  mirror,  FH,  only  partly  silvered,  called  the 
horizon  glass.  A  telescope  .K,  parallel  to  the  frame  and  pointed 
toward  the  center  of  horizon  glass,  helps  accuracy  of  observation. 
Shade  glasses  of  different  colors  and  density  (at  D  and  E}  make  it 
possible  to  observe  the  sun  under  all  varying  conditions  of  atmosphere 
—  haze,  fog,  thin  cloud,  or  a  perfectly  transparent  sky ;  for  that  orb 
is,  of  all  heavenly  bodies,  the  most  frequently  observed  in  navigation. 
Shade  glasses  tone  down  the  light,  whatever  its  intensity,  and  farther  in- 
crease the  accuracy  of  observation.  A  clamp  and  tangent  screw  (below 
the  arc)  facilitate  the  details  of  actual  observation ;  antecedent  to 
which,  however,  the  adjustments  of  the  sextant  must  be  carefully  made. 
The  most  important  are  these  :  when  the  arm  is  set  at  the  zero  of  the  arc, 
the  plane  of  the  principal  mirror  also  must  pass  through  the  zero  of  the 
arc ;  and  the  horizon  glass  must  be  parallel  to  the  mirror,  both  being 
perpendicular  to  the  plane  of  the  graduated  arc  or  limb.  The  horizon 
line  is  CH  (page  1,82),  and  the  heavenly  body  is  in  the  direction  CS. 


1 82  The  Astronomy  of  Navigation 

The  distant  horizon  is  seen  by  the  eye  through  the  telescope  at  A",  and 
its  line  of  sight  passes  through  the  upper  or  unsilvered  part  of  the  hori- 
zon glass  LL1 '.  When  the  arm  is 
at  o°,  the  index  glass  stands  in  the 
direction  A K\  but  when  an  altitude, 
HCS,  is  to  be  measured,  the  arm 
is  pushed  along  the  limb  to  O. 
The  index  glass  then  stands  in  the 
position  If,  so  that  light  will  travel 
in  the  direction  of  the  arrows  SABK. 
After  reflection  from  the  two  mir- 
rors, the  object  will  appear  in  contact 
with  the  horizon.  The  arc  is  read, 
and  the  observation  is  complete. 
As  the  angle  between  index  and 
horizon  glasses  is  half  the  angle 
How  Angles  are  measured  measured,  the  limb  is  graduated  at 

the  rate  of  i°  for  each  actual  30'. 

Finding  the  Latitude  at  Sea.  —  Usually  the  first  astro- 
nomical observation  at  sea  will  be  made  for  the  purpose  of 
finding  the  latitude  of  the  ship.  There  are  many  methods, 
but  all  are  based  on  the  fundamental  principle  already 
given,  that  the  latitude  is  always  equal  to  the  altitude  of 
the  celestial  pole.  Usually  latitude  is  found  by  observing 
the  altitude  of  some  celestial  body  when  crossing  the  me- 
ridian on  the  opposite  side  of  the  zenith  from  the  pole. 
So  it  is  referred  directly  to  the  equator,  whose  distance 
from  the  zenith  always  equals  the  latitude  also. 

For  example :  a  few  minutes  before  noon,  the  navigator  will  begin 
to  observe  the  sun's  altitude  with  the  sextant,  repeating  the  observation 
as  long  as  the  altitude  continues  to  increase.  When  the  sun  no  longer 
rises  any  higher,  it  is  on  the  local  meridian.  The  time  is  high  noon,  or 
apparent  noon.  The  officer  then  gives  the  order  l  Make  it  Eight  Bells,' 
and  proceeds  to  ascertain  the  latitude  from  the  observation  just  made. 
The  diagram  on  page  84  elucidates  the  principle  involved.  Once  the 
meridian  zenith  distance  is  found  by  observation,  latitude  is  ascertained 
from  it  by  the  same  principle,  whether  at  sea  or  on  land. 

Finding  the  Longitude  at  Sea.  —  As  on  land,  so  at  sea, 
finding  the  longitude  of  a  place  is  the  same  thing  as  find- 


Dip  of  the  Horizon  183 

ing  how  much  the  local  time  differs  from  the  time  of  a 
standard  meridian.  The  prime  meridian  of  Greenwich  is 
almost  universally  employed  in  navigation.  First, '  then, 
local  time  must  be  found. 

A  portable  instrument  like  the  sextant  must  be  used,  because  of  the 
continual  motion  of  the  ship.  With  it  the  navigator  observes  the  alti- 
tude of  some  familiar  heavenly  body  toward  the  east  or  west.  This 
operation  is  called  'taking  a  sight.'  Most  often  the  sun  is  observed  for 
this  purpose  —  either  early  in  the  morning,  or  late  in  the  afternoon. 
The  nearer  the  time  of  its  crossing  the  prime  vertical,  the  better,  because 
its  altitude  is  then  changing  most  rapidly,  and  so  the  observation  can  be 
made  more  accurately,  first,  the  latitude  must  be  known.  Then  the 
local  time  is  worked  out  by  a  branch  of  mathematics  called  spherical 
trigonometry.  This  computation  forms  part  of  the  everyday  duty  of  the 
navigator ;  and  as  simplified  for  his  use,  it  is  an  arithmetical  process, 
greatly  facilitated  by  specially  prepared  tables  of  the  relation  of  the 
quantities  involved.  These  are  three :  the  altitude  of  the  body  (given 
by  observation),  its  declination  (obtained  from  the  Nautical  Almanac), 
and  the  latitude  of  the  ship.  Having  found  the  local  time,  take  the 
difference  between  it  and  the  chronometer  (Greenwich)  time  ;  the  result 
is  the  longitude  sought.  If  local  time  is  greater  than  Greenwich  time, 
longitude  is  east;  west,  if  less.  There  are  many  methods  of  ascertain- 
ing longitude,  and  each  navigator,  as  a  rule,  has  his  favorite.  Sumner's 
method  is  generally  conceded  to  be  the  best.  Except  in  overcast 
weather,  the  navigating  officer  will  usually  feel  sure  of  the  position  of  his 
ship  within  two  miles  of  latitude,  and  three  to  five  miles  of  longitude.  It 
is  difficult  to  find  her  position  nearer  than  this  unless  the  observations 
are  themselves  made  with  exceptional  care,  and  the  errors  of  sextant 
and  chronometer  have  been  specially  investigated  with  greater  precision 
than  is  either  usual  or  necessary.  Once  the  position  of  the  ship  is 
known,  it  is  plotted  on  the  chart,  and  the  proper  course  is  calculated 
and  the  ship  maintained  on  it  by  constant  watch  of  the  compass,  a  deli- 
cate magnetic  instrument  by  which  true  north  can  always  be  found. 

Dip  of  the  Horizon.  —  In  calculating  any  observation  of 
altitude  of  a  heavenly  body  taken  at  sea,  a  correction  for 
dip  of  the  horizon  is  always  applied.  Dip  of  the  hori- 
zon is  the  angle  between  a  truly  horizontal  line  passing 
through  the  observer's  eye,  and  the  line  of  sight  to  his 
visible  horizon,  or  circle  which  bounds  the  view. 


1 84 


The  Astronomy  of  Navigation 


As  the  surface  of  our  globe  may  be  regarded  as  spherical  (always 
so  considered  in  practical  navigation),  it  must  curve  down  from  the 
ship  equally  in  every  direction.  The. figure  shows  this  clearly.  Also, 
as  altitude  is  angular  distance  above  the  sensible  horizon,  it  is  apparent 
that  every  observation  of  altitude  must  be  diminished  by  the  correction 
for  dip.  Plainly,  too,  dip  is  greater,  the  higher  the  deck  of  the  ship 
from  which  the  observation  is  taken.  If  the  deck  is  12  feet  above  the 
water,  the  correction  for  dip  is  about  three  minutes  of  arc;  if  18  feet, 
about  four  minutes.  From  the  elevation  of  a  deck  of  ordinary  height, 
the  visible  horizon  is  about  seven  miles  distant  in  every  direction ; 


Dip  of  the  Horizon 

and  generally  speaking  a  ship  will  never  be  visible  at  more  than  double 
this  distance,  even  with  a  telescope.  Usually  an  approaching  ship  will 
not  become  visible  until  about  eight  miles  away;  but  the  condition 
of  the  atmosphere,  the  character  of  the  distant  ship's  rigging,  the  way 
in  which  sunlight  falls  upon  it,  and  the  rising  and  falling  of  both  ships 
on  the  waves,  —  all  affect  this  distance  materially. 

Where  does  the  Southern  Cross  become  Visible  ?  —  A  question  of 
perennial  interest  to  the  southward  voyager.  Its  answer  may  come 
appropriately  now,  but  first  it  is  necessary  to  know  how  far  this  famous 
asterism  is  south  of  the  celestial  equator;  that  is,  its  south  declination. 
Consulting  charts  of  the  southern  heavens,  we  find  that  the  central 
region  of  the  Cross  is  in  south  declination  60°.  Consequently,  it  will 
just  come  to  the  southern  horizon  when  the  latitude  is  equal  to  90° 
—  60° ;  that  is,  30°.  But  haze  and  fog  near  the  sea  horizon  will  usually 
obscure  the  Cross  until  a  latitude  six  or  seven  degrees  farther  south 
has  been  reached.  Good  views  of  it  may  be  expected  at  the  Tropic 
of  Cancer,  and  they  improve  with  the  journey  farther  south.  It  must, 
however,  be  said  that  the  Southern  Cross  is  a  disappointment,  for  it 
is  by  no  means  so  striking  a  configuration  as  the  Great  Bear. 

Where  will  the  Sun  be  overhead  at  Noon  ?  —  Not  before 
we  reach  the  tropics,  because  the  sun  never  can  pass  over- 
head at  any  place  whose  latitude  exceeds  23-|-°. 


SoutJieru  Circumpolar  Stars 


But  in  Chapter  iv  it  was  shown  that  the  latitude  is  always  equal  to 
the  declination  of  the  zenith.  If,  therefore,  it  is  desired  to  find  the 
place  where  the  sun  will  pass  through  the  zenith  at  noon,  we  must 
first  ascertain  the  sun's  declination  from  the  almanac  (or  approximately 
from  page  85).  Then  it  is  apparent  that  the  zenith  sun  will  be  met  at 
noon,  when  the  latitude  of  the  ship  is  exactly  the  same  as  the  sun's 
declination.  From  vernal  equinox  to  autumnal  equinox,  when  the  sun 
is  all  the  time  north  of  the  equator,  the  ship  must  be  in  the  northern 
hemisphere,  in  order  that  the  sun  may  pass  directly  over  her.  And, 
in  general,  the  sun  will  pass  through  the  ship's  zenith  on  the  day  when 
her  latitude  is  the  same  in  sign  and  amount  as  the  declination  of  the 
sun.  For  example,  on  the  2d  of  March  the  sun  will  be  overhead  at 
noon  to  all  ships  which  are  crossing  the  7th  parallel  of  south  latitude, 
because  the  sun's  declination  is  7°  south  on  that  day. 

In  Southern  Latitudes.  —  Looking  northward,  or  away  from  the  pole 
now  visible,  the  stars  appear  to  rise  on  our  right  hand,  passing  up  over 
the  meridian,  and  setting  on 
our  left.  They  still  rise  in  the 
east  and  set  in  the  west.  But 
looking  poleward,  the  stars  cir- 
culate round  the  pole  clockwise 
by  diurnal  motion,  as  indicated 
by  arrows  in  the  diagram  adja- 
cent. The  south  pole  of  the 
heavens  rises  one  degree  above 
the  south  horizon  for  every 
higher  degree  of  south  lati- 
tude. If  the  south  pole  were 
actually  reached,  all  the  stars 
south  of  the  equator  would  be 
perpetually  visible,  and  no  star 
of  the  northern  hemisphere 
could  ever  be  seen.  But  the 
region  overhead  in  the  sky 
would  not  be  conspicuously 
marked, .as  at  the  north  pole, 
by  Polaris  and  the  Little  Bear, 
because  there  is  no  conspicuous 

south  polar  star.  In  fact,  there  is  no  star  as  bright  as  the  fifth  magni- 
tude within  the  circle  drawn  five  degrees  from  the  pole.  The  pair  of 
stars  in  the  Chamaeleon,  here  shown  underneath  the  pole,  are  of  the 
fifth  magnitude,  and  Beta  Hydri  is  a  third  magnitude  star.  All  are 
easy  to  find  from  the  Southern  Cross,  which  is  2|  times  farther  from 
the  pole  than  the  Chamaeleon  stars. 


Apparent  Motion  of  the  South  Polar  Heavens 


1 86  The  Astronomy  of  Navigation 

Rounding  Cape  Horn  to  San  Francisco.  —  On  the  remainder  of  our 
ship's  voyage  to  latitude  about  57°  south,  where  she  rounded  the  Cape, 
little  or  nothing  new  arose,  involving  any  astronomical  principle.  The 
Southern  Cross  passed  practically  through  the  zenith,  because  the  lati- 
tude was  nearly  equal  to  the  declination  of  the  asterism.  The  mild 
temperature  nearly  all  the  way  was  a  verification  of  the  opposite 
season  in  the  southern  hemisphere ;  for  although  it  was  winter  (De- 
cember, January,  and  February)  at  home,  it  was  summer  at  the  same 
time  in  south  middle  latitudes.  Approaching  the  equator,  it  was 
observed  that  the  inequality  of  day  and  night  was  gradually  obliterated, 
quite  independently  of  the  season ;  for  at  the  equator  the  diurnal  arcs 
of  all  heavenly  bodies  are  exact  semicircles,  no  matter  what  their 
declination.  At  the  equator,  too,  the  brief  twilight  attracted  attention  — 
brief  because  the  sun  sinks  at  right  angles  to  the  horizon,  instead  of 
obliquely  ;  so  that  it  reaches  as  quickly  as  possible  the  angle  of  depres- 
sion (18°)  below  the  horizon,  at  which  twilight  ceases.  On  approaching 
the  California  coast,  after  a  voyage  of  nearly  four  months,  in  which  land 
had  been  sighted  only  once,  it  was  a  matter  of  much  concern  what  the 
deviation  of  the  chronometers  might  be  from  the  rates  established  at 
New  York.  It  was  evidently  not  large,  for  the  landfall  off  the  Golden 
Gate  was  made  without  any  uncertainty.  On  coming  to  anchor  in  San 
Francisco  bay,  it  was  easy  to  verify  the  chronometers,  by  observing  the 
time  signal  at  local  noon  (nearly)  each  day,  which  is  given  by  the 
dropping  of  a  large  and  conspicuous  time  ball  at  exactly  8h.  om.  6s. 
P.M.,  Greenwich  time.  Comparison  of  the  chronometers  with  this 
signal  showed  that  the  Greenwich  time,  as  indicated  by  their  dials, 
differed  only  8s.  from  the  time  ball;  so  that  the  average  daily  devia- 
tion from  the  rate  as  determined  at  New  York  was  only  ^  of  a  second. 

Standard  Time  Signals.  —  About  a  dozen  time  balls  are 
now  in  operation  in  the  United  States.  The  principal 
ones  are  dropped  every  day  at  noon,  Eastern  Standard  or 
75th  meridian  time,  in  Boston,  New  York,  Philadelphia, 
Baltimore,  and  Washington ;  at  noon,  Central  time,  in 
New  Orleans;  and  at  noon,  Pacific  Standard,  or  i2Oth 
meridian  time,  in  San  Francisco. 

The  error  of  the  signal,  only  a  fraction  of  a  second,  is  published  in 
the  local  newspapers  of  the  following  day.  In  foreign  countries,  time 
signals  are  now  regularly  furnished,  chiefly  for  the  convenience  of  ship- 
ping, in  about  125  of  the  principal  ports  of  the  world.  In  England 
and  the  British  possessions,  it  is  customary  to  give  the  time  signal  at 


Where  Does  the  Day  Change  ?  187 

i  P.M.,  often  by  firing  a  gun.  But  the  dropping  of  a  time  ball  (page  9) 
is  the  favorite  signal  throughout  the  world  generally.  In  many  of  these 
ports,  the  time  is  determined  with  precision  at  a  local  observatory,  and 
the  time  ball  may  be  utilized  in  re-rating  the  ship's  chronometers. 

Where  does  the  Day  change  ?  —  Imagine  a  railway  gir- 
dling the  world  nearly  on  the  parallel  of  New  York,  and 
equipped  with  locomotives  capable  of  maintaining  a  speed 
of  800  miles  an  hour.  At  noon  on  Wednesday,  start  west- 
ward from  New  York ;  in  about  an  hour,  reach  Chicago,  in 
another  hour  Denver,  in  still  another  hour  San  Francisco. 
As  these  places  are  about  15°,  or  one  hour  of  longitude 
from  each  other,  evidently  it  will  be  Wednesday  noon  on 
arrival  at  each  of  them,  and  at  all  intermediate  points, 
because  the  traveler  is  going  westward  just  as  fast  as  the 
earth  is  turning  eastward ;  so  it  will  be  perpetual  midday. 
Continue  the  journey  westward  at  the  same  rate  all  the 
way  round  the  earth.  Night  will  not  come  because  the  sun 
has  not  set.  So  there  can  be  no  midnight.  How,  then, 
can  the  day  change  from  Wednesday  to  Thursday?  Will 
it  still  be  Wednesday  noon  when  the  traveler  returns  to 
New  York  ?  On  arrival  there,  24  hours  after  he  started, 
he  will  be  told  that  it  is  Thursday  noon.  Where  did  the 
day  change  ?  Manifestly  it  must  change  somewhere  once 
every  24  hours.  Nearly  the  whole  world  has  agreed  to 
change  at  the  iSoth  meridian  from  Greenwich,  because 
there  is  little  land  adjacent  to  this  meridian,  and  very  few 
people  are  inconvenienced.  Noon  at  Greenwich  is  mid- 
night on  the  iSoth  meridian.  If,  therefore,  a  ship  westward 
bound  on  the  Pacific  Ocean  comes  to  this  meridian  at  mid- 
night of,  say,  Wednesday,  on  crossing  that  meridian  it  is 
immediately  after  12  A.M.  of  Friday.  As  a  rule  ships  will 
not  arrive  at  the  iSoth  meridian  exactly  at  midnight;  but 
this  does  not  affect  the  principle  involved :  a  whole  day, 
or  24  hours,  is  dropped  or  suppressed  in  every  case. 


OF  THE 
TTTvTTTTTP 


1 88  The  Astronomy  of  Navigation 

If,  for  example,  it  is  Friday  afternoon  at  four  o'clock  when  this  line 
is  reached,  it  becomes  Saturday  immediately  after  4  P.M.  as  soon  as 
the  i Both  meridian  is  crossed.  This  experience,  familiar  to  all  trans- 
pacific voyagers,  is  called  '  dropping  the  day.'  If  a  person  born  on 
the  29th  of  February  were  crossing  the  Pacific  Ocean  westward  on  a 
leap  year,  and  should  arrive  at  the  iSoth  meridian  at  midnight  on  the 
28th  of  February,  the  change  of  day  would  bring  the  reckomng^of  time 
forward  to  the  first  of  March ;  so  that  he  would  have  the  novel  experi- 
ence of  living  eight  years  with  strictly  but  a  single  birthday  anniversary. 
Journeying  eastward  across  the  iSoth  meridian,  the  reverse  of  this  pro- 
cess is  followed,  and  24  hours  are  subtracted  from  the  reckoning.  If, 
for  example,  the  ship  reaches  this  meridian  at  10  A.M.  Wednesday,  it 
immediately  becomes  10  A.M.  Tuesday  on  crossing  it.  When,  in  1867, 
the  United  States  purchased  Alaska,  it  was  found  necessary  to  set  the 
official  dates  of  the  new  territory  forward  11  days  (page  166),  because 
the  reckoning  had  been  brought  eastward  from  Russia,  its  former  owner. 

Time  at  Home  compared  with  Time  in  Japan.  —  The 
arrival  of  a  ship  at  Yokohama  will  usually  be  cabled  to  her 
owners,  —  in  New  York,  very  probably.  Sending  such 
a  message  naturally  gives  rise  to  inquiry  as  to  when  it 
will  be  received ;  for  there  is  no  cable  across  the  Pacific 
Ocean,  and  the  dispatch  must  cross  Asia,  Europe,  and 
the  Atlantic.  The  table  of  '  Standard  Time  in  Foreign 
Countries'  (page  126)  shows  that  the  time  service  of  the 
Japanese  Empire  corresponds  to  the  13  5th  meridian  (9 
hours)  east  of  Greenwich.  As  Eastern  Standard  time  is 
five  hours  slower  than  Greenwich  time,  evidently  Japan  is 
10  hours  west  of  our  standard  meridian ;  and  its  standard 
time  would  be  10  hours  slower  than  ours,  except  for  the 
change  of  day.  On  account  of  this,  the  standard  time  of 
Japan  is  24  hours  in  advance,  minus  10  hours  slower ;  that 
is,  14  hours  in  advance  of  Eastern  Standard  time. 

The  same  result  is  reached,  if 'we  go  round  the  world  eastward  to 
Japan,  thereby  avoiding  the  troublesome  iSoth  meridian.  The  Eastern 
Standard  meridian  is  five  hours  west  of  Greenwich,  and  Japan  is  nine 
hours  east  of  Greenwich.  So  that  it  is  14  hours  east  of  us ;  that  is,  its 
time  is  14  hours  faster  than  ours.  Allow  six  hours  of  actual  time  for  the 
transmission  of  a  cablegram  from  Yokohama  to  New  York ;  if  one 


Great  Circle  Courses  189 

were  sent  at  7  A.M.  on  Tuesday,  it  would  be  delivered  at  n  P.M.  on 
Monday,  or  seemingly  eight  hours  before  it  was  dispatched. 

Great  Circle  Courses  the  Shortest  in  Distance.  —  In  ocean 
voyages,  in  steamships,  particularly  in  crossing  the  Pacific, 
the  captain  will  usually  choose  the  course  which  makes 
his  run  the  shortest  distance  between  the  two  ports.  Im- 
agine a  plane  through  the  center  of  the  earth  and  both 
ports ;  the  arc  in  which  this  plane  cuts  the  earth's  surface 
is  part  of  a  great  circle.  This  arc,  the  shortest  distance 
between  the  two  ports,  is  called  a  great  circle  course.  If 
both  are  on  the  equator,  the  equator  itself  is  the  great 
circle  connecting  them ;  and  the  ship  goes  due  east  or  due 
west,  when  sailing  a  great  circle  course  from  one  to  the 
other.  If,  however,  the  ports  are  not  on  the  equator, 
but  both  in  middle  latitudes,  as  San  Francisco  and  Yoko- 
hama, the  parallel  of  latitude 
(which  nearly  joins  them  and 
is  a  small  circle  of  the  globe) 

'    San  Francisco  Yokohama 

has  a  greater  degree  of  cur- 
vature than  the  great  circle,    E     ^ — — -,    w 

Which         Clearly        mUSt         paSS    San  Francisco  Yokohama 

through      much      higher      latl-  Great  Circle  Course  the  Shortest 

tudes.  As  shown  by  the  dia- 
gram of  the  two  arcs,  seen  from  above  the  pole,  the  great 
circle  arc,  lying  farther  north,  deviates  less  from  a  straight 
line  than  the  corresponding  arc  of  a  parallel  (upper  curve). 
It  is  therefore  a  shorter  distance.  Consequently  ships 
sailing  great  circle  courses  will  usually  pass  through  lati- 
tudes higher  than  either  the  point  of  departure  or  des- 
tination. 

Before  passing  on  to  a  study  of  sun,  moon,  and 
planets,  we  digress  to  consider  the  instruments  by  whose 
aid  our  knowledge  of  these  orbs  has  mainly  been  ac- 
quired. 


CHAPTER   IX 

THE  OBSERVATORY  AND   ITS   INSTRUMENTS 

^vBSERVATORIES  are  buildings  in  which  astro- 
y^^/  nomical  and  physical  instruments  are  housed,  and 
which  contain  all  the  accessories  for-  their  con- 
venient use.  Most  important  of  all  instruments  of  a 
modern  observatory  are  telescopes  and  spectroscopes. 

Astronomy  before  the  Days  of  Telescopes.  —  The  prog- 
ress of  astronomy  has  always  been  closely  associated  with 
the  development  and  application  of  mechanical  processes 
and  skill.  Earlier  than  the  seventeenth  century,  the  size  of 
the  planets  could  not  be -measured,  none  of  their  satellites 
except  our  moon  were  known,  the  phases  of  Mercury  and 
Venus  were  merely  conjectured,  and  accurate  positions  of 
sun,  moon,  and  planets  among  the  stars,  and  of  the  stars 
among  themselves,  were  impossible  —  all  because  there 
were  no  telescopes.  More  than  a  half  century  elapsed 
after  the  invention  of  the  telescope  before  Picard  com- 
bined it  with  a  graduated  circle  in  such  a  way  that  the 
measurement  of  angles  was  greatly  improved.  Then  arose 
the  necessity  for  accurate  time ;  but  although  Galileo  had 
learned  the  principles  governing  the  pendulum,  astronomy 
had  to  wait  for  the  mechanical  genius  of  Huygens  before 
a  satisfactory  clock  was  invented,  about  1657.  Nearly  all 
the  large  reflecting  telescopes  ever  built  were  constructed 
by  astronomers  who  possessed  also  great  facility  in  practi- 
cal mechanics ;  and  the  rapid  and  significant  advances  in 
nearly  all  departments  of  astronomy  during  the  last  half 

190 


Best  Sites  for  Observatories  1 9 1 

century  would  not  have  been  possible,  except  through  the 
skill  and  patience  of  glass  makers,  opticians,  and  instru- 
ment builders,  whose  work  has  reached  almost  the  limit  of 
perfection.  Before  1860,  if  we  except  the  meager  evidence 
from  meteoric  masses  of  stone  and  iron,  some  of  which  had 
actually  been  seen  to  fall,  it  is  proper  to  say  that  our  igno- 
rance of  the  physical  constitution  of  other  worlds  than  ours 
was  simply  complete.  The  principles  of  spectrum  analysis 
as  formulated  by  Kirchhoff  led  the  way  to  a  knowledge  of 
the  elements  composing  every  heavenly  body,  no  matter 
\vhat  its  distance,  provided  only  it  is  giving  out  light  in- 
tense enough  to  reach  our  eyes.  But  since  Newton,  no 
necessary  step  had  been  taken  along  this  road  until  the 
way  to  this  signal  discovery  was  paved  by  the  deftness  of 
Wollaston,  who  showed  that  light  could  not  be  analyzed 
unless  it  is  first  passed  through  a  very  narrow  slit ;  and 
of  Fraunhofer,  the  eminent  German  optician,  who  first 
mapped  dark  lines  in  the  spectrum  of  the  sun.  So,  too, 
in  our  own  day  the  power  of  telescope  and  spectroscope 
has  been  vastly  extended  by  the  optical  skill  and  mechani- 
cal dexterity  of  the  Clarks  and  Rowland,  Hastings  and 
Brashear,  all  Americans. 

Best  Sites  for  Observatories —  An  observatory  site 
should  have  a  fairly  unobstructed  horizon,  as  much  free- 
dom from  cloud  as  possible,  good  foundations  for  the 
instruments,  and  a  very  steady  atmosphere. 

All  of  these  conditions  except  the  last  are  self-evident.  To  realize 
the  necessity  of  a  steady  atmosphere,  look  at  some  distant  out-door 
object  through  a  window  under  which  is  a  register,  a  stove,  or  a  radi- 
ator. It  appears  blurred  and  wavering.  Similarly,  currents  of  warm 
air  are  continually  rising  from  the  earth  to  upper  regions  of  the  at- 
mosphere, and  colder  air  is  coming  down  and  rushing  in  underneath. 
Although  these  atmospheric  movements  are  invisible  to  the  eye,  their 
effect  is  plainly  visible  in  the  telescope  as  blurring,  distortion,  quiver- 
ing, and  unsteadiness  of  celestial  objects  seen  through  these  shift- 


192        The  Observatory  and  its  Instruments 

ing  air  strata  of  different  temperatures,  and  consequently  of  different 
densities.  The  trails  on  photographic  star  plates,  exposed  with  the 
camera  at  rest,  make  this  very  evident.  That  a  perfect  telescope  may 
perform  perfectly,  it  must  be  located  in  a  perfect  atmosphere.  Other- 
wise its  full  power  cannot  be  employed.  All  hindrances  of  atmosphere 
are  most  advantageously  avoided  in  arid  or  desert  regions  of  the  globe, 
at  elevations  of  3000  to  10,000  feet  above  sea  level.  On  the  American 
continent  have  been  established  several  observatories  at  mountain  ele- 
vation, the  most  important  being  the  Boyden  Observatory  of  Harvard 


The  Dearborn  Observatory  at  Evanston,  Professor  G.  W.  Hough,  Director 

College,  Arequipa,  Peru  (8000  feet)  ;  the  Lowell  Observatory,  Arizona 
(7000  feet)  ;  and  the  Lick  Observatory,  California  (4000  feet).  Higher 
mountains  have  as  yet  been  only  partially  investigated ;  and  it  is  not 
known  whether  difficulties  of  occupying  them  permanently  would  more 
than  counterbalance  the  gain  which  greater  elevation  would  afford. 

A  Working  Observatory.  —  Chief  among  exterior  features  is  the  great 
dome,  usually  hemispherical,  and  capable  of  revolving  all  the  way 
round  on  wheels  or  cannon  balls.  The  opening  through  which  the 
telescope  is  pointed  at  the  stars  is  a  slit,  two  or  three  times  as  broad  as 
the  diameter  of  the  object  glass.  The  slit  opens  in  a  variety  of  ways, 
often  as  in  the  above  picture,  by  sliding  to  one  side  on  pivots  and 
rollers.  Solidly  built  up  in  the  center  of  the  tower  is  a  massive  pier, 
to  support  the  telescope,  wholly  disconnected  from  the  rest  of  the  build- 
ing. By  means  of  the  universal  or  equatorial  mounting  (page  54),  the 


Instruments  Classified  193 

open  slit,  and  the  revolving  dome,  the  telescope  is  readily  directed 
toward  any  object  in  the  sky.  Observatories  are  provided  with  a 
meridian  room,  with  a  clear  opening  from  north  to  south,  in  which  a 
transit  instrument  or  meridian  circle  is  mounted.  Part  of  it  shows  at 
the  right  of  the  tower.  Here  also  are  the  chronograph,  and  clock  or 
chronometer  for  recording  transits  of  the  heavenly  bodies.  Modern 
observatories  are  provided  with  a  library  and  computing  room,  a  photo- 
graphic dark  room,  and  other  accessories  of  equipment,  varying  with 
the  nature  of  their  work.  The  best  typ^  of  observatory  construction 
utilizes  a  minimum  of  material,  so  that  very  little  heat  from  the  sun  is 
stored  in  its  walls  during  the  day,  and  local  disturbance  of  the  air  in 
the  evening,  caused  by  radiation  of  this  heat,  is  but  slight.  Louvers 
and  ivy-grown  walls  contribute  much  to  this  desirable  end.  It  is  con- 
sidered best  to  house  each  instrument  in  a  suitable  structure  of  its  own, 
as  remote  as  possible  from  many  or  massive  buildings. 

Instruments  classified.  —  Instruments  used  in  astronomi- 
cal observatories  are  divided  into  three  classes :  — 

(a)  Telescopes,  or  instruments  for  aiding  or  increasing 
the  power  of  the  human  eye.  There  are  two  kinds,  the 
dioptric,  or  refracting  telescope,  and  the  catoptric,  or  re- 
flecting telescope. 

($)  Instruments  for  measuring  angles.  These,  also,  are 
subdivided  into  two  kinds ;  the  arc-measuring  instruments, 
like  graduated  circles,  for  measuring  very  large  arcs,  the 
micrometer  for  measuring  very  small  ones,  and  the  helio- 
meter  for  measuring  arcs  intermediate  in  value,  as  well 
as  very  small  ones.  The  second  class  of  instruments 
concerned  in  the  measurement  of  angles  are  transit  instru- 
ments for  observing  tirne^measured  by  the  uniform  angu- 
lar motion  of  a  point  on  the  equator),  chronographs  for 
recording  the  time,  clocks  and  chronometers  for  carrying 
the  time  along  accurately  and  continuously  from  day  to 
day. 

(c]  Physical  instruments,  of  which  many  varieties  are  em- 
ployed in  most  modern  observatories,  for  investigating  the 
light  and  heat  radiated  from  celestial  objects.  Chief  among 
them  are  spectroscopes,  or  light-analyzing  instruments,  of 
TODD'S  ASTRON. —  13 


194       The  Observatory  and  its  Instruments 

which  there  are  numerous  forms,  adapted  to  especial 
uses.  Heliostats  are  plane  mirrors  moved  by  clockwork, 
for  the  purpose  of  throwing  a  reflected  beam  of  light  from 
a  heavenly  body  in  a  constant  direction.  The  bolometer 
is  an  exceedingly  sensitive  measurer  of  heat,  and  the 
thermopile  is  used  for  the  same  purpose,  though  much 
less  sensitive.  The  photometer  is  used  for  measuring  the 
light  of  the  heavenly  bodies.  The  actinometer  and  pyrhe- 
liometer  are  physical  instruments  used  in  measuring  the 
heat  of  the  sun.  The  photographic  camera  is  extensively 
employed  at  the  present  day,  to  secure,  by  means  of  tele- 
scope, photometer,  spectroscope,  and  bolometer,  permanent 
record,  unaffected  by  small  personal  errors  to  which  all 
human  observations  are  subject. 

Telescopes.  —  The  telescope  is  an  optical  instrument  for 
increasing  the  power  of  the  eye  by  making  distant  objects 
seem  larger  and  therefore  nearer. 


Illustrating  the  Visual  Angle 

It  does  this  by  apparently  increasing  the  visual  angle.  A  distant 
object  fills  a  relatively  small  angle  to  the  naked  eye,  but  a  suitable 
combination  of  lenses,  by  changing  the  direction  of  rays  coming  from 
the  object,  makes  it  seem  to  fill  a  much  larger  angle,  and  there- 
fore to  be  nearer.  Such  a  combination  is  called  a  telescope.  The 
parts  of  all  telescopes  are  of  two  kinds,  —  optical  and  mechanical. 
The  optical  parts  are  lenses,  or  mirrors,  according  to  the  kind  of  tele- 
scope ;  and  the  mechanical  parts  are  tubes,  and  various  appliances  for 
adjusting  the  lenses  or  mirrors,  including  also  the  machinery  for  point- 
ing the  tube.  All  the  different  lenses  used  in  telescopes  are  illustrated 
opposite  (in  section) .  One  principle  is  the  same  in  all  telescopes : 
a  lens  or  mirror  (called  the  objective)  is  used  to  form  near  at  hand 
an  image  of  a  distant  object ;  and  between  image  and  eye  is  placed 


Kinds  of  Telescopes 


195 


EQUI-CONVEX 


MENISCUS 


a  microscope  (called  the  eyepiece  or  ocular)  for  looking  at  the  image  — 
just  as  if  it  were  a  fly's  wing,  or  the  texture  of  a  feather.  The  point  to 
which  the  lens  converges  the  parallel  rays  from  a  star  is  called  the 
principal  focus  (illustra- 
tion below) .  The  central 
ray,  which  passes  through 
the  centers  of  curvature 
of  the  two  faces  of  the 
lens,  traverses  a  line  called 
the  optical  axis.  The 
plane  passing  through  the 
principal  focus  perpendic-  PLAN0' 
ular  to  the  optical  axis  is 
called  the  focal  plane. 
Objective  and  eyepiece 
must  be  so  adjusted  and 
secured  that  their  axes 
shall  lie  accurately  in  a 
single  straight  line.  If 
objective  and  eyepiece 
could  be  held  in  this  posi- 
tion by  hand,  also  at  the 
right  distance  apart,  there 
would  be  no  need  of  a  tube.  The  tube  is  sometimes  made  square,  as 
well  as  round,  and  is  to  be  regarded  simply  as  a  mechanical  necessity 


PLANO-CONCAVE 


EQUI-CONCAVE 


CONCAVO-CONVEX 


Lenses  of  Different  Shapes  (in  Section) 


A  Convex  Lens  refracts  Parallel  Rays  to  the  Principal  Focus 

for  keeping  the  optical  parts  of  the  telescope  in  proper  relative  position. 
Also  the  tube  is  of  some  use  in  screening  extraneous  light  from  the 
eyepiece,  although  that  service  is  slight. 

Kinds  of  Telescopes.  —  As  to  the  principal  kinds   of  telescopes : 
(a)   If  the  objective  is  a  lens  (in  its  simplest  form  an  equi-convex 


196       The  Observatory  and  its  Instruments 

lens),  then  the  image  is  produced  by  bending  inward  or  refracting  to 
the  focus  all  rays  of  light  which  strike  the  lens ;  and  the  telescope 
is  called  a  refractor,  or  refracting  telescope.  This  sort  of  instrument 
appears  to  have  been  first  known  in  Holland,  early  in  the  seventeenth 
century ;  also  it  was  invented  by  Galileo  in  1609,  and  first  used  by  him 
in  observing  the  heavenly  bodies.  If  a  telescope  is  to  perform  prop- 
erly, its  object  glass  cannot  be  made  of  plate  glass,  because  the  eye- 
piece would  reveal  defects  in  it  similar  to  those  which  the  eye  plainly 
sees  in  ordinary  window  glass.  But  the  objective  must  be  made  of 
that  finest  quality  known  as  optical  glass.  Through  a  perfect  speci- 


V 

Angle  of  Reflection  equals  Angle  Concave  Mirror  reflects  Parallel 

of  Incidence  Rays  to  Focus 

men  of  optical  glass  polished  with  parallel  sides,  a  perpendicular  ray 
of  light  will  pass  without  appreciable  refraction,  and  with  very  little 
absorption.  (£)  If  the  objective  is  a  concave  mirror  or  speculum,  the 
image  is  then  formed  by  reflection,  to  the  focus,  of  all  rays  of  light 
which  fall  upon  the  highly  polished  surface  of  the  mirror,  and  the  tele- 
scope is  called  a  reflector,  or  reflecting  telescope.  The  above  figures 
show  the  principle  involved,  the  angle  of  reflection  being  in  every  case 
equal  to  angle  of  incidence.  An  actual  speculum  may  be  regarded  as 
made  up  of  an  infinite  number  of  plane  mirrors,  arranged  in  a 
concave  surface  differing  slightly  from  that  of  a  sphere,  and  being 
in  section  a  parabola  (page  398).  As  shown  in  the  next  illustration 
the  focal  point  is  halfway  from  mirror  to  center  of  curvature. 

Growth  of  the  Refracting  Telescope.  —  An  ordinary  convex  lens,  in 
converging  rays  of  light  to  a  focus,  must  refract  them,  or  bend  them 
toward  the  axis  of  the  lens.  But  light  is  commonly  composed  of  a 
variety  of  colored  rays,  ranging  through  the  spectrum  from  red  to 
violet.  Soon  after  the  invention  of  the  telescope  Sir  Isaac  Newton 
discovered  by  experiment  that  prisms  do  not  bend  rays  of  different 
color  alike  ;  violet  light  is  much  more  strongly  refracted  than  red,  and 
intermediate  colors  in  different  proportions,  according  to  the  kind  of 
light  employed.  We  may  regard  a  lens  as  an  infinitely  large  collec- 


Growth  of  Refracting  Telescope 


197 


tion  of  tiny  prisms.  Clearly,  then,  a  perfect  telescope  seemed  to  be 
an  impossibility  from  the  very  nature  of  the  case,  because  no  single 
lens  had  power  to  gather  all  rays  at  a  given  focus,  and  could  only 
scatter  them  along  the  axis  —  the  focus  for  violet  rays  being  nearest 
the  object  glass,  and  for  the  red  farthest  from  it  However,  by  grind- 


Focus  halfway  from  Mirror  to  Center  of  Curvature 

ing  the  convex  lens  almost  flat,  so  that  its  focal  length  became  very 
great,  this  serious  hindrance  to  development  of  the  telescope  was  in 
part  overcome,  and  many  telescopes  of  bulky  proportions  were  built 
during  the  I7th  century,  which  were  most  awkward  and  almost  im- 
possible to  manipulate.  Sometimes  the  object  glass  was  mounted  in 
a  universal  joint  on  top  of  a  high  pole,  and  swung  into  the  proper 
direction  by  means  of  a  cord,  drawn  taut  by  the  observer  who  held 
the  eye-lens  in  his  hand  as  best  lie  could.  Telescopes  were  built  over 


BEAM  OF  WHITE  LIGHT 


BEAM  OF  WHITE  LIGHT 


RED 


A  Prism  both  refracts  and  disperses  White  Light 

200  feet  in  length,  and  some  observations  of  value  were  made  with 
them,  though  at  an  inconceivable  expenditure  of  time  and  patience. 
Newton  concluded  that  it  was  hopeless  to  expect  a  serviceable  tele- 
scope of  this  kind;  so  the  minds  of  inventors  were  turned  in  other 
directions. 


198       The  Observatory  and  its  Instruments 

Why  a  Single  Lens  is  not  Achromatic.  —  For  the  sake  of  clear  ex- 
planation, regard  the  lens  made  up  as  in  the  last  figure,  so  that  a  section 
of  it  is  the  same  as  a  section  of  two  triangular  prisms  placed  base  to  base. 
Let  two  parallel  beams  of  white  light  fall  upon  the  prisms  as  shown. 
Each  will  then  be  refracted  toward  the  axis  of  the  lens,  and  at  the  same 
time  decomposed  into  the  various  colors  of  the  spectrum.  Red  rays 
being  refracted  least,  their  focus  will  be  found  farthest  from  the  lens. 
Violet  rays  undergoing  the  greatest  angular  bending,  their  focus  will 
be  nearest  the  lens.  Foci  for  the  other  colors  will  be  scattered  along 
the  axis  as  indicated.  If  we  consider  the  actual  lens,  with  an  infinitude 
of  faces  or  prisms,  the  effect  is  the  same.  So  that,  speaking  generally, 
it  cannot  be  said  that  the  lens  brings  the  rays  of  white  light  to  any 
single  focus  whatever,  and  the  image  of  a  white  object  will  be  variously 
colored,  wherever  the  eyepiece  may  be  placed. 

Principle  of  the  Achromatic  Telescope.  —  The  two  lenses 
of  the  objective  must  be  of  different  kinds  of  glass  :  (i)  a 
double-convex  lens  of  crown  glass,  not  very  dense,  which 
ordinarily  the  light  passes  through  first ;  (2)  a  plano-con- 
cave lens  of  dense  flint  glass,  usually  .placed  close  to  the 
crown  lens  in  small  telescopes. 


FOCUS  FOR 
COMBINATION 


Illustrating  Principle  of  Achromatic  Object  Glass 

Similar  prisms  of  these  two  kinds  of  glass  bend  the  rays  about  equally  ; 
so  that  while  the  double-convex  lens  converges  the  rays  toward  the 
axis,  the  single  or  plano-concave  diverges  them  again,  by  an  amount 
half  as  great.  So  much  for  refraction  merely :  and  it  is  plain  from  the 
above  figure  that  the  double  object  glass  must  have  a  greater  focal  length 
on  account  of  the  diverging  effect  of  the  flint  lens.  Next  consider 
the  effect  of  the  two  lenses  as  to  dispersion  of  light,  and  the  colors 
which  each  would  produce  singly.  If  we  try  equal  prisms  of  the  two 
kinds  of  glass,  it  is  found  that  the  flint,  on  account  of  its  greater  den- 
sity, produces  a  spectrum  about  twice  as  long  as  the  crown ;  therefore 


Efficiency  of  Object  Glasses 


199 


its  dispersive  power,  prism  for  prism,  is  twice  as  great.  Now  a  lens 
may  be  regarded  as  composed  of  a  multitude  of  prisms,  —  a  mosaic  of 
indefinitely  small  prisms.  Evidently,  then,  the  plano-concave  lens  of 
flint  glass,  although  it  has  only  half  the  refracting  power  of  the  crown 
lens,  will  produce  the  same  degree  of  color  as  the  double-convex  lens 
of  crown  glass.  Therefore,  the  dispersion  or  color  effect  of  the  con- 
vergent crown  lens  is  neutralized  by  the  passing  of  the  rays  through 
the  divergent  flint  lens,  and  a  practically  colorless  image  is  the  result. 
Thus  is  solved  the  important  problem  of  refraction  without  dispersion, 
opening  the  way  for  the  great  refractors  of  the  present  day. 

History  of  the  Achromatic  Telescope.  —  Half  a  century  after  Newton, 
Hall  in  1 733  found  that  the  color  of  images  in  the  refractor  could  be 
nearly  eliminated  by  making  the  object  glass  of  two  lenses 
instead  of  one,  as  just  explained ;  a  significant  invention 
usually  attributed  to  Dollond,  who  about  1760  secured  a 
patent  for  the  same  idea  which  had  occurred  to  him  in- 
dependently. Progress  of  the  art  of  building  telescopes 
was  thus  assured ;  and  the  only  limitation  to  size  appeared 
to  be  the  casting  of  large  glass  disks.  About  1840,  these 
obstacles  were  first  overcome  by  glass  makers  in  Paris ; 
but  in  the  larger  telescopes,  a  new  trouble  arose,  inherent 
in  the  glass  itself;  for  the  ordinary  form  of  double  object 
glass  cannot  be  made  perfectly  achromatic.  An  intense 
purple  light  surrounds  bright  objects,  an  effect  of  the  sec- 
ondary spectrum,  as  it  is  called,  because  dispersion  or 
decomposition  of  the  crown  glass  cannot  be  exactly  neu- 
tralized by  recomposition  of  the  flint.  Farther  progress, 
then,  was  impossible  until  other  kinds  of  glass  were  in- 
vented. Recent  researches  by  Abbe  under  the  auspices 
of  the  German  Government  have  led  to  the  discovery  of 
many  new  varieties  of  glass,  by  combining  which  object 
glasses  of  medium  size  have  already  been  made  almost 
absolutely  achromatic.  Hastings  in  America  and  Taylor 
in  England  have  met  with  marked  success.  Some  of  the 
new  objectives  are  made  of  two  lenses,  and  others  of  three  ; 
but  there  is  great  difficulty  in  procuring  very  large  disks 
of  this  new  glass. 

Efficiency  of  Object  Glasses.  —  This  depends  upon  two 
separate  conditions :  (a)  the  light-gathering  power  of  Achromatic 
an  objective  is  proportional  to  its  area.  Theoretically  a 
6-inch  glass  will  gather  four  times  as  many  rays  as  a  3-inch 
objective,  because  areas  of  objectives  vary  as  the  squares  of  their 
diameters.  But  practically  the  light  of  the  larger  glass  will  be  some- 
what reduced,  because  of  the  thicker  lenses ;  for  all  glass,  no  matter 


2OO       The  Observatory  and  its  Instruments 


how  pure,  is  slightly  deficient  in  transparency.  In  the  same  way,  the 
light-gathering  power  of  any  lens  may  be  compared  with  that  of  the 
naked  eye.  In  the  dark,  the  pupil  of  the  average  eye  expands  to 
a  diameter  of  about  \  inch.  The  ratio  of  its  diameter  to  that  of  a 

3-inch  glass  is  15,  as  in 
the  illustration  (reduced 
^)  ;  so  a  star  in  a  3-inch 
telescope  appears  nearly 
225  times  brighter  than 
it  does  to  the  naked  eye. 
Calculating  in  the  same 
way  the  efficiency  of  the 
great  4o-inch  lens  of  the 
Yerkes  Observatory,  it  is 
found  to  be  40,000  times 
that  of  the  eye.  Test 
light-gathering  power  by 
ascertaining  the  faintest 
stars  visible  in  the  tele- 
scope, and  comparing  with 
lists  of  suitable  objects. 
(£)  The  defining  power 
of  an  objective  is  partly 
its  ability  to  show  fine 
details  of  the  moon  and 
planets  perfectly  sharp 
and  clear ;  but  more  precisely  it  is  the  power  of  separating  the  component 
members  of  close  double  stars  (page  452).  This  power  varies  directly 
with  the  size  or  diameter  of  object  glasses,  if  they  are  perfect ;  that  is 
a  6-inch  glass  will  divide  a  double  star  whose  components  are  o".8 
apart,  whereas  it  will  require  a  1 2-inch  glass  to  separate  a  double  star 
of  only  o". 4  distance.  But  defining  power  is  quite  as  dependent  upon 
perfection  of  the  original  disks  of  glass,  as  upon  the  skill  and  patience 
of  the  optician  who  has  ground  and  polished  them.  A  large  defect  of 
either  makes  a  worthless  telescope. 

Method  of  Testing  a  Telescope.  —  Unscrew  the  cell  of  the  objective 
from  the  tube,  but  do  not  take  the  lenses  out  of  the  cell.  If  on  looking 
through  it  at  the  sky,  the  glass  appears  clear  and  colorless,  or  nearly  so, 
the  light-gathering  power  may  be  regarded  as  satisfactory.  Small 
specks  and  air  bubbles  will  never  be  numerous  enough  to  be  harmful ; 
each  only  obstructs  a  small  pencil  of  light  equal  to  its  are.:..  The  defin- 
ing power  may  be  tested  in  a  variety  of  ways.  Following  is  the  method 
by  an  artificial  star :  Point  the  telescope  on  the  bulb  of  an  ordinary 
thermometer  which  lies  in  the  sunshine,  50  feet  or  more  distant.  Or 


Eye  and  Objective  collect  Rays  in  Proportion 
to  their  Areas 


A  Small  but   Useful  Telescope 


201 


the  convex  bottom  of  a  broken  bottle  of  dark  glass  may  be  used,  R  in 
the  illustration.  On  focusing,  an  artificial  star  will  appear,  due  to  re- 
flection of  the  sun  from  the  bulb,  sometimes  surrounded  by  diffraction 
rings  (A,  below).  Slide  eyepiece  inward  and  outward  from  focus, 


u 


u 


One  Method  of  Testing  a  Telescope 


until  bright  point  of  light  spreads  out  into  a  round  luminous  disk, 
B.  This  is  called  the  spectral  image.  A  dark  center,  when  the  eye- 
piece is  pulled  out,  and  a  brighter  central  area  when  pushed  in,  show 
that  curvature  of  the  glasses  is  more  or  less  imperfect.  A  spectral 
image  having  a  piece  cut  out,  or  a  brush  of  scattering  light,  is  a  sign 
of  bad  defects  inherent  in  the  glass  itself.  An  excellent  objective  gives 
spectral  images  perfectly  circular,  and  evenly  illuminated 
throughout,  B.  Repeat  these  tests  on  stars  of  the  first 
magnitude.  Heat  from  a  lighted  lamp  placed  where  shown 
will  simulate  many  deleterious  effects  of  a  very  unsteady 
atmosphere.  A  and  B  then  become  C  and  D,  rays  and 
spots  of  the  latter  being  continually  in  motion. 

A  Small  but  Useful  Telescope.  —  By  expending  a  few 
cents  for  lenses,  a  person  of  average  mechanical  ability 
may,  by  a  few  hours1  work,  become  possessed  of  a  telescope 
powerful  enough  to  show  many  mountains  on  the  moon, 
spots  on  the  sun,  satellites  of  Jupiter,  and  a  few  of  the 
wider  double  stars.  Buy  from  an  optician  two  spectacle 
lenses,  round  rather  than  oval,  and  of  very  different  pow- 
ers ;  for  instance,  No.  5  and  No.  30.  These  numbers 
express  the  focal  lengths  of  the  lenses.  Fit  together 
two  pasteboard  tubes  so  that  one  will  slide  inside  the  other  quite 
smoothly.  Their  combined  length  must  be  about  six  inches  greater 


Spectral 
Images 


2O2       The  Observatory  and  its  Instruments 

than  the  sum  of  the  numbers  of  the  two  lenses.  Blacken  the  inside 
of  tubes,  and  attach  the  lenses  to  their  outside  ends.  No.  30  being 
the  objective,  and  pointed  toward  the  object,  the  magnifying  power  of 
the  two  lenses,  when  separated  by  a  distance  equal  to  the  sum  of  their 
focal  lengths,  will  be  equal  to  their  ratio,  or  six  diameters.  It  was  with 
a  telescope  made  in  this  way  that  the  writer,  when  a  boy  of  fourteen, 
got  his  first  glimpse  of  the  satellites  of  Jupiter.  A  few  dollars  will  buy 
a  good  achromatic  object  glass  (of  perhaps  two  inches  diameter)  and  a 
pair  of  suitable  eyepieces  (powers  about  25  and  100).  A  suitable 
mounting  for  such  telescopes  has  already  been  described  on  page  53. 
The  most  important  optical  requisite  is  stated  at  the  middle  of  page 
195.  On  adjusting  the  lenses  in  the  tube,  a  serviceable  and  convenient 
telescope  will  be  provided,  quite  capable  of  showing  the  phases  of 
Venus,  the  ring  of  Saturn,  and  numerous  double  stars. 

The  Great  Refractors.  —  At  the  head  of  the  list  stands 
the  4O-inch  telescope,  65  feet  long,  of  the  Yerkes  Observa- 
tory (pages  7  and  15).  More  favorably  located  is  its  rival 
in  size,  the  famous  Lick  telescope  of  36  inches  aperture, 
situated  on  the  summit  of  Mount  Hamilton,  California, 
4300  feet  above  the  sea. 

The  mountings  or  machinery  for  both  these  great  instruments  were 
built  in  Cleveland,  by  Messrs.  Warner  &  Swasey;  but  the  object 
glasses  were  made  by  the  celebrated  firm  .of  Alvan  Clark  &  Sons,  of 
Cambridgeport,  from  glass  disks  manufactured  in  Paris.  No  optical 
glass  of  the  highest  quality  has  yet  been  made  in  America,  the  process 
being,  in  some  essentials,  secret.  Steinheil  of  Munich  is  now  construct- 
ing an  objective  of  3 1  \  inches  aperture,  of  the  new  glass,  for  the  astro- 
physical  observatory  near  Berlin.  A  glass  of  like  dimension  by  Henry 
is  at  the  Meudon  Observatory.  Paris.  The  Clarks  have  made  also  an 
objective  of  30  inches  aperture,  mounted  by  Repsold,  at  the  Russian 
Observatory  of  Pulkowa,  near  Saint  Petersburg.  A  glass  of  equal  size, 
figured  by  the  Brothers  Henry  of  Paris,  is  mounted  at  the  splendid 
observatory  founded  by  Bischoffsheim  at  Nice,  in  the  south  of  France. 
A  29  inch  by  Martin  is  at  the  Paris  Observatory.  The  next  three  tele- 
scopes were  made  at  Dublin,  by  Sir  Howard  Grubb,  one  of  28  inches 
and  one  of  26  inches  aperture,  located  at  the  Royal  Observatory,  Green- 
wich, and  the  other,  of  27  inches,  at  Vienna.  Following  these  in  order 
are  a  pair  of  telescopes  of  26  inches  aperture,  made  by  Alvan  Clark  & 
Sons,  one  of  which  is  the  principal  instrument  of  the  United  States 
Naval  Observatory,  at  Washington,  and  the  other  is  located  at  the 
University  of  Virginia.  Between  the  dimensions  of  25  inches  and  15 


Growth  of  the  Reflecting  Telescope         203 

inches  there  are  about  two  dozen  refracting  telescopes  in  all,  many 
of  which  were  made  by  Alvan  Clark  &  Sons,  although  Brashear  of 
Alleghany,  an  optician  of  the  first  rank,  has  made  an  1  8-inch  glass, 
now  at  the  University  of  Pennsylvania.  Quite  the  opposite  of  re- 
flectors, it  is  noteworthy  that  most  of  the  great  refractors  have  been 
built  in  America;  and  that  they  have  contributed  in  a  more  marked 
degree  to  the  progress  of  astronomical  science. 

Invention  and  Growth  of  the  Reflecting  Telescope.  —  If  converging 
the  rays  of  light  by  refraction  could  never  make  a  perfect  telescope, 
clearly  the  only  method  left  was  to  gather  them  at  a  focus  by  reflection 
from  a  highly  polished  surface.  Although  this  way  of  making  a  tele- 
scope seems  to  have  been  understood  as  early  as  1639,  still  a  quarter 
century  elapsed  before  Gregory  built  the  first  one  (1663).  He  used 


RAYS  FROM 
A  STAR 


==:—  ^lUIIIIIIimmH"!!!—  jt 


GREGORIAN  (Secondary  Mirror  Concave) 


RAYS  FROM 
A  STAR 


CASSEGRAINIAN  (Secondary  Mirror  Convex) 
EYE 

a,  


NEWTONIAN  (Eyepiece  on  side  of  tube) 
Three  Types  of  Reflecting  Telescope 

two  concave  mirrors  as  in  the  illustration ;  the  one  large  to  form  the 
image,  and  the  other  small  to  reflect  the  rays  out  of  the  tube  to  the 
eyepiece.  Ten  years  later  Cassegrain  made  a  farther  improvement, 
replacing  the  small  concave  mirror  of  Gregory  by  a  convex  one  (shown 
in  the  illustration  also).  Both  these  forms  of  reflector  have  the  advan- 
tage that  the  observer  looks  directly  toward  the  object  at  which  the 
telescope  is  pointed  ;  but  there  is  a  great  disadvantage  in  that  the  center 
or  best  part  of  the  mirror  has  to  be  cut  away,  in  order  to  let  the  rays 
through  it  to  the  eyepiece.  The  mirror  is  left  whole,  and  less  of  its 
light  is  sacrificed  in  the  form  invented  by  Newton  (1672),  who  inter- 
posed a  small  flat  mirror,  at  an  angle  of  45°  with  the  axis  of  the  larger 
mirror.  This  arrangement,  most  commonly  used  in  reflecting  tele- 
scopes at  the  present  day,  has  a  slight  disadvantage  in  that  the  observer 
must  look  into  the  eyepiece  at  right  angles  to  the  direction  of  the  ob- 
ject under  examination  (see  figure)  ;  but  a  small  right-angled  or  totally 


204       The  Observatory  and  its  Instruments 

reflecting  prism  is  now  universally  employed  in  lieu  of  the  little 
diagonal  mirror,  thereby  saving  a  large  percentage  of  light.  A  fourth 
form  of  reflector,  first  suggested  by  Le  Maire,  was  used  by  Herschel, 
in  the  latter  part  of  the  i8th  century;  he  tilted  the  speculum  slightly, 
to  bring  its  focus  at  side  of  tube.  Axis  of  eyepiece  is  directed,  not  as 
in  diagram  below,  but  toward  center  of  mirror.  Tilting  the  mirror 
saves  all  light,  but  distortion  of  image  is  not  easy  to  avoid.  Recently 


RAYS      FRO  I 
A     STAR 


Le  Mairean  or  Herschelian  Reflecting  Telescope 

the  '  brachy-telescope,'  or  short  telescope,  has  been  invented  to  ever- 
come  this  difficulty,  by  second  reflection  from  a  small  and  oppositely 
inclined  convex  mirror.  Down  to  the  middle  of  the  I9th  century, 

specula  were  always  made  of  an 
alloy,  generally  composed  of  59 
parts  of  tin  and  126  of  copper. 
Specula  are  now  almost  univer- 
sally made  of  glass,  with  a  very 
thin  film  of  silver  deposited 
chemically  upon  the  front  sur- 
face, not  upon  the  back  as  in 
the  common  mirror.  These 
telescopes  are  often  called  silver- 
on-glass  reflectors.  As  the  light 
does  not  pass  through  the  glass, 
it  may  be  much  inferior  in  quality 
to  that  required  for  a  lens.  Be- 
cause less  difficult  to  build,  the 
great  telescope  of  the  future  will 
probably  be  a  reflector,  although 
of  inferior  definition.  Great  re- 
fractors are,  however,  less  clumsy 
The  Great  Paris  Reflector  '(Martin)  and  more  effective  for  actual  use. 


Reflectors  and  Refractors  Compared        205 


The  Great  Reflecting  Telescopes.  —  The  largest,  sometimes  called  the 
'  leviathan,' was  built  by  the  late  Lord  Rosse  in  1845  at  Birr  Castle, 
Parsonstown,  Ireland.  The  speculum  is  of  metal,  six  feet  in  diameter, 
and  about  eight  inches  thick.  Its  excessive  weight  of  four  tons  makes  a 
very  heavy  mounting  necessary.  Lord  Rosse's  telescope  is  Newtonian 
in  form.  The  giant  tube  is  56  feet  long,  and  7  feet  in  diameter.  The 
next  in  size  is  a  five-foot  silver-on-glass  reflector,  built  by  Common 
in  1889  at  Ealing,  England.  It  is  Cassegrainian  in  form,  and  the 
glass  of  the  mirror  is  nearly  one  foot  in  thickness,  in  order  to  pre- 
vent flexure,  or  bending  by  its  own  weight.  The  Yerkes  Observatory 
is  constructing  a  reflector  of  equal  size.  In  1867  Thomas  Grubb  built  a 
four-foot  silver-on-glass  '  Gregorian '  for  the  observatory  at  Melbourne, 
Australia,  and  it  is  perhaps  the  most  convenient  in  use  of  all  the 
great  reflectors.  In  the  latter  part  of  the  i8th  century  Sir  William 
Herschel  built  numerous  reflecting  telescopes,  among  them  one  of  four 
feet  diameter,  and  another  of  half  that  size ;  he  made  many  important 
discoveries  with  them,  but  none  are  now  in  condition  to  use.  Lassell, 
an  eminent  English  astronomer,  built  two  great  reflectors,  one  of  four 
feet,  and  the  other  of  two  feet  aperture,  which  he  used  on  the  island 
of  Malta,  1852-1865.  Several  reflectors,  three 
feet  aperture,  have  been  constructed,  the  most 
important  of  which  is  owned  by  the  present 
Lord  Rosse ;  also  one  by  the  Lick  Observa- 
tory. At  the  Paris  Observatory  is  a  great 
silver-on-glass  reflector  of  nearly  four  feet 
aperture  ;  and  an  instrument  ten  feet  in  diam- 
eter has  been  projected  rfor  the  Paris  Exposi- 
tion of  1900.  It  is  interesting  to  note  that 
none  of  these  great  instruments  have  been 
constructed  in  America.  The  largest  reflector 
ever  built  in  the  United  States  is  28  inches 
in  diameter.  It  was  made  by  Henry  Draper, 
New  York,  in  1871,  and  is  now  used  at  the 
Harvard  Observatory.  Among  present 
builders  of  reflecting  telescopes  in  America 
are  Edgecomb  of  Mystic,  Connecticut ;  and 
Brashear,  one  of  whose  lesser  instruments  is 
pictured  in  the  adjoining  illustration. 

Reflectors  and  Refractors  compared.  —  In 
reflectors  of  medium  size,  tarnish  and  de- 
terioration of  the  polished  surface  are  the 
chief  disadvantage  But  the  film  of  a  mirror 
less  than  a  foot  in  diameter  is  readily  renewed. 
When  freshly  silvered,  a  1 2-inch  speculum  will  collect  the  same  amount 


A  Modern  '  Newtonian'  by 
Brashear 


206       The  Observatory  and  its  Instruments 

of  light  as  a  1 2-inch  object  glass,  loss  by  reflection  from  the  former 
being  about  equal  to  loss  by  absorption  in  passing  through  the  latter. 
Well  figured  and  newly  polished  mirrors  of  no  greater  dimension  than 
this  usually  perform  excellently ;  and  there  is  a  marked  advantage  from 
the  gathering  of  rays  of  all  colors  at  the  same  focus.  But  from  12 
inches  upward,  flexure  of  the  mirror  begins  to  cause  difficulties  which 
increase  rapidly  with  the  size  of  the  speculum.  The  mirror  may  be 
given  a  perfect  parabolic  figure  for  the  position  in  which  it  is  polished ; 
but  as  soon  as  turned  to  another  angle  of  elevation,  gravity  distorts 
its  figure.  As  a  result,  rays  from  a  star  are  not  collected  at  a  single 
point,  but  scattered  round  it.  The  larger  the  mirror,  the  greater  this 
difficulty,  becoming  almost  impossible  to  alleviate  entirely.  Glass 
mirrors,  in  order  to  be  least  affected  by  it,  should  have  a  thickness 
equal  to  one  sixth  of  their  diameter.  With  object  glasses,  on  the  other 
hand,  bending  of  the  lens  by  its  own  weight  in  different  positions  has 
not  been  found  to  affect  appreciably  the  character  of  images  formed  by 
any  of  the  great  glasses,  except  the  4o-inch,  which  suffers  a  slight  de- 
formation of  images  in  certain  positions.  Still,  it  must  be  remembered 
that  the  objective,  although  called  achromatic,  is  not  completely  so; 
and  in  some  of  the  very  large  refractors,  the  intense  blue  light  sur- 
rounding a  bright  object  is  often  a  serious  obstacle  in  the  work  of 
practical  observation.  On  the  whole,  the  refractor  is  generally  pre- 
ferred to  the  reflector.  It  is  easier  to  adjust  and  keep  in  order;  and 
its  tube  being  closed,  it  is  much  less  subject  to  harmful  effect  of  local 
air  currents.  It  is  a  fact,  too,  that  more  than  three  fourths  of  all  the 
work  of  astronomical  observation  has  been  done  with  refracting 
telescopes.  • 


Path  of  Rays  through  a  Negative  (Huygenian)  Eyepiece 

The  Eyepiece.  —  The  eyepiece  of  a  telescope  is  simply  a  magnify- 
ing glass,  or  microscope  for  examining  the  image  of  an  object  formed 
at  the  focus  by  the  objective.  Any  small,  convex  lens,  then,  may 
be  used  as  an  eyepiece,  but  its  effective  field  of  view  is  very  limited. 


The  Eyepiece 


207 


So  a  combination  of  two  plano-convex  lenses  is  usually  employed,  in 
order  that  the  field  may  be  enlarged,  and  vision  be  distinct  everywhere 
in  that  field.  Two  forms  of  celestial  eyepiece  are  common,  called  the 
negative  and  the  positive  eyepiece.  Both  forms  have  a  smaller,  or 
eye  lens,  and  a  larger,  or  field  lens ;  the  latter  toward  the  objective, 
the  former  nearer  the  eye.  In  the  negative  (sometimes  called  from 
Huygens,  its  inventor,  the  Huygenian)  eyepiece,  both  eye  lens  and 
field  lens  have  their  flat  faces  turned  toward  the  eye,  as  in  the 


Path  of  Rays  through  a  Positive  (Ramsden)  Eyepiece 

preceding  figure.  In  the  positive  (called,  also,  from  its  inventor  the 
Ramsden)  eyepiece,  the  convex  faces  of  both  lenses  are  turned  inward, 
or  toward  each  other,  as  in  the  above  figure,  where  the  eye  lens  is  drawn 
double  its  proper  diameter.  The  negative  eyepiece  has  its  focus  be- 
tween the  two  lenses.  The  focus  of  the  positive  eyepiece  lies  beyond 
both  lenses,  a  short  distance  toward  the  objective.  Positive  eyepieces 
are  always  used  for  transit  instruments  and  micrometers.  Both  these 
forms  of  eyepiece  do  not  themselves  invert,  but  when  employed  in  con- 
junction with  an  object  glass,  they  show  all  objects  inverted,  the  objective 


RAYS 

FROM  * 

OBJECTIVE 


Path  of  Rays  through  a  Terrestrial  or  Erecting  Eyepiece 


itself  causing  the  inversion,  because  the  rays  cross  in  passing  through  it. 
A  terrestrial  or  day  eyepiece  is  one  which,  when  employed  with  an  object 
glass,  shows  all  objects  right  side  up.  The  re-inversion  of  the  image 
necessary  to  effect  this  is  produced,  as  shown  in  the  preceding  illustra- 
tion, by  constructing  the  eyepiece  of  four  lenses  instead  of  two.  Dif- 
ferent eyepieces  of  different  magnifying  powers  may  generally  be  used 
with  the  same  objective,  by  means  of  suitable  draw-tubes,  called 
adapters.  The  same  eyepiece  can  be  used  in  either  reflectors  or  refrac- 
tors. 


208       The  Observatory  and  its  Instruments 

To  ascertain  the  Magnifying  Power.  —  Following  is  an  easy  method : 
Select  a  convenient  object  marked  with  dividing  lines  at  pretty  regular 
intervals  — clapboards  on  a  house,  bricks  in  a  wall,  or  better  the  joints 
where  plates  of  tin  are  lapped  on  a  roof.  When  the  sun  is  shining 
obliquely  across  them,  set  up  the  telescope  as  distant  as  possible,  yet 
near  enough  so  that  the  joints  can  readily  be  counted  with  the  naked 
eye.  Then  point  the  telescope  at  the  roof.  Look  at  it  through  the 
eyepiece  with  one  eye,  and  with  the  other  look  along  the  outside  of 
the  telescope  at  the  roof  also ;  first  with  one  eye,  then  with  the  other, 
then  with  both  together.  Amplification,  or  magnifying  power  (at  that 
distance  of  the  telescope  from  the  roof)  is  equal  to  the  degree  of  this 
enlargement ;  and  it  can  be  ascertained  by  simply  counting  the  number 
of  divisions  (as  seen  by  the  naked  eye)  which  are  embraced  between 
any  two  adjacent  joints  as  seen  in  the  telescope.  The  two  images 
of  the  same  object  will  be  seen  superposed,  and  a  little  practice  will 
enable  one  to  make  the  count  with  all  necessary  accuracy.  Good  tele- 
scopes are  usually  provided  with  an  assortment  of  eyepieces  whose  magni- 
fying powers  range  approximately  between  seven  and  70  for  each  inch  of 
aperture  of  the  object  glass.  For  example,  a  four-inch  telescope  would 
have  perhaps  four  eyepieces,  magnifying  about  25,  90,  200,  and  300  times. 

How  to  measure  Small  Angles.  —  The  micrometer  is  an  instrument 
for  measuring  small  angles.  It  is  attached  to  the  telescope  in  place  of 


A  Modern  Micrometer  with  Electric  Illumination  (Ellery^ 

the  eyepiece.  The  illustration  shows  all  the  important  working  parts. 
Crossing  the  oblong  field  of  view  are  seen  two  spider  lines  (aa),  with 
which  the  measuring  is  done.  All  parts  of  the  micrometer  are  so  de- 
vised and  related  that  these  two  lines  can  be  seen  at  night  in  the 
dark  field  of  view ;  moved  with  accuracy  slowly  toward  or  from  each 
other;  and  their  exact  position  recorded.  In  the  best  modern  microm- 
eters, either  the  lines  or  the  field  of  view  can  be  illuminated  at  will  by 
a  small  incandescent  electric  lamp  (£)•  The  spider  lines  are  attached 
to  separate  sliding  frames ;  each  frame  can  be  moved  by  a  thumb- 


The   Transit  Instrument 


209 


screw,  the  head  of  which  projects  outside  the  micrometer  box.  One 
of  these,  called  the  micrometer  screw,  has  enlarged  heads  (hlh*) 
graduated  to  show  the  number  of  turns  and  fraction  of  a  turn  of  this 
screw.  The  eyepiece  (not  shown)  is  a  positive  one  attached  to  the 


A  Compact  Modern  Transit  Instrument  (from  a  Design  by  Heyde) 

micrometer  box  in  front  of  the  sliding  frames.  To  measure  a  small  arc,  — 
for  example,  the  diameter  of  a  planet  —  point  the  telescope  so  that  the 
disk  of  the  planet  appears  in  the  center  of  the  field  of  view.  Then  turn 
the  two  thumbscrews  until  the  spider  lines  are  both  seen  tangent  to 
opposite  sides  of  the  disk  at  the  same  time.  Read  the  micrometer-head. 
TODD'S  ASTRON.  —  14 


2io       The  Observatory  and  its  Instruments 


Then  turn  the  micrometer-screw,  until  the  two  lines  appear  as  one. 
Read  the  head  again ;  take  the  difference  of  readings,  and  multiply  it 
by  the  arc-value  of  one  turn  (which  must  have  been  previously  deter- 
mined). Resulting  is  the  diameter  of  the  planet  in  arc. 

The  Transit  Instrument.  —  Soon  after  the  invention  of  the  telescope, 
early  in  the  I7th  century,  an  instrument  was  devised  by  a  Danish 

astronomer,  Roemer,  which  has  now  sup- 
planted nearly  every  other  for  determining 
time  with  precision.  It  is  called  the 
transit  instrument,  because  used  in  observ- 
ing the  passage,  or  transit,  of  heavenly 
bodies  across  the  field  of  view.  Ordinarily 
it  is  mounted  in  a  north  and  south  line. 
On  top  of  the  two  rigid  triangular  piers 
(preceding  page)  are  bearings  in  which  the 
axis  of  the  transit  instrument  turns.  The 
telescope  .F  is  secured  at  right  angles  to 
the  axis  C.  When  turned  round  in  its 

bearings,  the  telescope  describes  the  plane  of  the  meridian.  On  that 
account  it  is  sometimes  called  a  meridian  transit.  In  the  convenient 
type  of  transit  here  pictured,  the  axis  forms  half  of  the  telescope  tube. 
A  glass  prism  in  the  central  cube  reflects  the  rays  through  C  to  the  eye 
at  the  left:  Such  an  instrument  is  often  called  a  'broken  transit.' 
Until  the  instrument  is  reversed,  the  eye  remains  stationary,  no  matter 
what  the  declination  of  the  star  observed. 

Observing  with  the  Transit  Instrument.  —  First,  it  must  be  adjusted. 
A  level,  L,  hanging  below,  makes  the  axis  horizontal.  In  the  field  of 
view  is  a  reticle,  often  made  of  spider  lines,  but  sometimes  by  ruling 
very  fine  lines  with  a  diamond  point  on  a  thin  plate  of  optical  glass. 


Adjustable  Reticle 


RETICLE  OBJECT  GLASS 

To  show  the  Line  of  Collimation 

The  reticle  is  accurately  adjusted  in  focal  plane  of  object  glass,  and  in 
smaller  instruments,  surveyor's  transits,  for  example,  lines  are  arranged 
as  in  the  two  illustrations  above.  The  lines  are  often  called  threads 
or  wires.  The  line  of  collimation  is  the  line  from  the  center  of  object 
glass  to  the  central  intersection  of  lines  of  reticle.  This  line  is  ad- 
justed perpendicular  to  the  axis  of  revolution  of  the  telescope.  Then  by 
repeated  trials  upon  stars,  the  Y's,  or  bearings,  are  shifted  very  slightly 
north  or  south,  on  pivots  (page  209)  under  the  left-hand  end  of  the 


Reticle  of  Transit 


The  Astronomical  Clock  21 

:A\K 

base,  until  the  axis  lies  precisely  east  and  west.  When  the  foregoing 
adjustments  have  been  made,  the  telescope,  or  more  accurately  the  line 
of  collimation,  swings  round  in  the  true  plane  of  the  meridian.  To 
observe  a  star,  count  the  beats  of  the  clock 
while  looking  in  the  field  of  view ;  and  set 
down  the  second  and  tenth  of  its  crossing 
the  central  vertical  line  of  the  reticle.  In  the 
illustration  a  star  is  seen  approaching  the 
vertical  or  transit  lines.  If  a  very  accurate 
value  is  desired,  observe  the  passage  over 
the  five  central  lines,  and  then  take  the 
average.  This  will  be  the  time  required. 

The  Astronomical  Clock.  —  Timepieces  used  in  observatories  are  of 
two  kinds,  clocks  and  chronometers.  One  or  the  other  is  indispensable. 
The  astronomical  clock  has  a  pendulum  oscillating  once  each  second : 
if  it  oscillates  once  a  sidereal  second,  it  is  a  sidereal  clock ;  if  once  a 
mean  solar  second,  it  is  a  mean  time  clock.  A  seconds  hand  records 
each  oscillation.  Also  it  has  hour  and  minute  hands,  like  ordinary 

clocks,  except  that  the  dial  is 
usually  divided  into  24  hours 
instead  of  12,  for  the  conven- 
ience of  the  astronomer,  in 
recording  hours  of  the  astro- 
nomical day,  or  in  following  the 
stars  according  to  right  ascen- 
sion. If,  at  any  instant,  the 
clock  does  not  show  exact 
time,  the  difference  between 
true  time  and  clock  time  is 
called  the  correction,  or  error 
of  the  clock.  This  must  be 
found  from  day  to  day,  or  from 
night  to  night,  by  observing 
transits  of  the  heavenly  bodies 
with  the  meridian  circle  or  the 
transit  instrument.  If  a  clock 
does  not  keep  exact  pace  with 
the  objects  of  the  sky,  it  is 
said  to  have  a  rate.  As  with  the  chronometer,  daily  rate  is-  the  amount 
by  which  the  error  changes  in  24  hours.  A  large  rate  is  inconvenient, 
"  but  does  not  necessarily  imply  a  bad  clock.  The  less  the  rate  changes 
the  better  the  clock.  Dampness  of  th£  air  and  sudden  changes  of 
temperature  are  hostile  to  the  fine  performance  of  timekeepers  of 
every  sort.  Equality  of  surrounding  conditions  is  secured  as  much 


I 


View  into  Clock-room  (Lick  Observatory) 


2 1 2        The  Observatory  and  its  Instruments 


as  possible  by  keeping  clocks  and  chronometers,  as  the  last  illustration 
shows,  in  a  small  and  separate  room,  where  the  air  may  readily  be  kept 
dry  and  its  temperature  nearly  constant. 

Pendulum  and  Escapement.  —  Horology  is  the  science  which  em- 
braces everything  pertaining  to  measurement  of  time,  and  to  mechani- 
cal contrivances  for  effecting  this  end.  The  chronometer  is  described 
and  pictured  in  the  preceding  chapter  (page  171).  Accurate  running  of 
a  clock  is  dependent  mainly  upon  two  parts  of  its  mechanism,  (a)  the 

pendulum,  and  (b)  the  escape- 
ment. The  pendulums  of  all 
observatory  and  standard 
clocks  are  compensated  for 
temperature,  so  that  the 
natural  fluctuations  of  this 
element  may  have  little  or  no 
effect  upon  the  length  of  the 
pendulum,  and  therefore  upon 
its  period  of  oscillation. 
There  is  a  variety  of  methods 
by  which  the  compensation 
is  effected.  The  illustration 
shows  the  simplest  of  them. 
The  steel  pendulum  rod 
passes  through  a  zinc  tube 
(shaded),  to  the  bottom  of 
which  is  attached  the.  heavy 
pendulum-bob.  With  a  rise 
of  temperature,  the  down- 
ward expansion  of  the  steel 
is  just  equalized  by  the  up- 
ward expansion  of  the  zinc; 
so  the  center  of  oscillation 
remains  at  the  same  distance 
from  the  point  of  support. 
The  center  of  oscillation  is 

that  point  of  a  pendulum  in  which,  if  the  whole  mass  of  the  pendulum 
were  concentrated,  the  period  of  oscillation  would  not  vary.  The  grid- 
iron pendulum  and  the  mercurial  pendulum  are  other  forms  of  compen- 
sation. Next  in  importance  to  the  pendulum  is  the  escapement.  The 
illustration  represents  in  outline  one  of  the  best  forms.  It  is  called 
the  gravity  escapement,  because  the  pendulum  is  driven  by  the  pressure 
alternately  of  two  gravity  arms,  which  are  swung  aside  by  the  six  black 
pins  in  the  hub  of  the  escapement  wheel.  The  clock  train  does  the 
work  of  raising  the  arms  outward  from  the  pendulum  rod ;  so  that  the 


Compensation 
Pendulum 


Gravity  Escapement 


The  Chronograph 


213 


pendulum  swings  almost  perfectly  free,  having  no  work  to  do  except 
to  raise  the  gravity  arms  just  enough  to  trip  the  escapement  at  the 
smoothly  polished  jewels  A  A. 

The  Chronograph.  —  In  recording  transits  of  the  heavenly  bodies, 
greater  convenience,  rapidity,  and  precision  are  attained  by  using  the 
chronograph,  a  mechanical  contrivance  first  devised  by  American 
astronomers  about  1850,  and  now  used  in  observatories  universally. 
The  illustration  shows  an  excellent  type  of  this  instrument.  The 
chronograph  consists  of  a  cylinder  about  8  inches  in  diameter  and 


A  Modern  Chronograph  by  Warner  &  Swasey 

1 6  inches  in  length,  which  revolves  once  every  minute  at  a  uniform 
speed.  Wound  upon  it  is  a  sheet  of  blank  paper,  and  above  it  trails 
a  pen  connected  with  an  armature,  so  that  every  vibration  of  the  pen- 
dulum, by  closing  an  electric  circuit,  joggles  the  pen  or  throws  it  aside  a 
fraction  of  an  inch  at  the  beginning  of  each  second.  The  illustration 
(next  page)  shows  a  small  part  of  a  chronograph  sheet,  full  size.  As 
the  barrel  or  cylinder  revolves,  the  pen  carriage  travels  slowly  along,  so 
that  the  trail  of  the  pen  is  a  continuous  spiral  round  the  barrel,  with 
60  notches  or  breaks  in  every  revolution.  In  the  circuit  of  the  pen 
armature  is  a  small  push  button,  called  an  observing  key.  This  is  held 
in  the  hand  of  the  observer  while  the  star  is  passing  the  field.  When- 
ever it  crosses  a  spider  line,  a  tap  of  the  observing  key  records  the 
instant  automatically  on  the  chronograph  paper,  which  may  be  removed 
and  read  at  leisure.  As  is  apparent  from  the  illustration,  tenths  of  a 
second  are  readily  estimated,  even  without  any  measuring  scale.  The 
breaks  at  regular  intervals  are  made  automatically  by  the  timepiece. 
The  short  breaks  between  A  and  B  are  made  in  quick  succession  by 


214       The  Observatory  and  its  Instruments 

the  observer,  to  show  that  a  star  is  just  coming  to  the 
lines.  Transit  of  the  star  over  the  first- two  lines  took 

/5s  place  at  C  (7  h.  16  m.  7.4  s.),  and  at  D  (7  h.  16  m.  1 1.4  s.), 
reading  in  all  cases  from  the  preceding  (or  lower)  side  of 

j^s  the  break.  By  transits  of  ten  stars  of  five  lines  each,  a 
good  observer  can  determine  the  error  of  his  timepiece 
within  two  or  three  hundredths  of  a  second.  Hough  has 
recently  perfected  -a  printing  chronograph  which  records 
the  time  in  figures  on  a  paper  fillet. 

4%s  Personal  Equation.  —  Few  observers,  no  matter  how 
practiced,  tap  the  key  exactly  when  a  star  is  crossing  a 

MS  line.  Most  of  them  make  the  record  just  after  the  star 
has  crossed,  and  still  others  always  press  the  button  a 
small  fraction  of  a  second  before  the  star  reaches  the 

^  wire.  It  does  not  matter  how  much  too  early  or  too  late 
the  record  is  made,  because  the  difference  can  usually  be 

gs  found  by  methods  known  to  the  practical  astronomer ; 
but  a  good  observer  is  one  who  makes  this  difference 

os  invariable  ;  that  is,  his  personal  equation  should  be  a  con- 
stant quantity.  The  personal  equation  of  an  observer 
is  the  difference  between  his  record  of  any  phenomenon, 

ys  and  the  thing  itself.  In  observing  transits  of  heavenly 
bodies,  most  observers  have  a  personal  equation  amount- 

6s  ing  to  one  or  two  tenths  of  a  second  of  time.  Personal 
equation  is  usually  found  by  observing  with  a  personal 

rs  equation  machine,  an  instrument  which  records  on.  a 
single  chronograph  sheet,  not  only  the  observer's  time  of 
transit,  but  also  the  absolute  instant  when  the  star  is 

4-s  crossing  the  lines.  The  next  illustration  shows  such  a 
machine.  Light  from  the  lamp  on  the  right  provides  an 

js  artificial  star  which  the  clockwork  makes  to  travel  across 
the  lines  in  front  of  the  observing  tube  on  the  left.  Abso- 
8  lute  time  is  time  corrected  for  personal  equation.  It  is 
nearly  always  required  in  the  accurate  determination  of 
longitudes  by  the  electric  telegraph. 

1s  The  Photo-chronograph.  —  As  the  effect  of  personality 
is  usually  absent  from  all  records  made  by  photography, 

0*  many  attempts  have  been  made  to  register  star-transits 
by  photographic  means.  The  instrument  which  does  this 
takes  the  place  of  both  eyepiece  and  chronograph,  and 
is  called  the  photo-chronograph.  Opposite  is  a  picture 
Part  of  the  of  this  ingenious  little  instrument.  If  a  photographic 
plate  is  firmly  fixed  in  the  focal  plane  of  a  transit  instru- 
ment, and  a  star  is  allowed  to  move  through  the  field,  the 


The  Photo-chronograph 


215 


Machine  for  determining  Personal  Equation  (Eastman) 

negative  will  show  a  fine,  dark  line  or  trail,  crossing  the  plate  hori- 
zontally from  west  to  east.  By  holding  a  lantern  in  front  of  the  object 
glass  a  few  seconds,  the  ver- 
tical lines  in  the  field  may 
also  be  obtained  on  the  same 
plate.  There  will  be,  then, 
an  absolute  record  of  the 
star's  path  through  the  field 
and  across  the  lines;  but 
nothing  will  be  known  as  to 
the  time  when  the  star  was 
crossing  any  particular  line. 
Now  instead  of  fastening  the 
plate,  insert  it  in  a  little 
frame  which  slides  north  and 
south  a  small  fraction  of  an 
inch.  So  arrange  the  details 
of  the  mechanism  that  an 
armature  will  move  the  frame 
automatically.  Connect  this 
armature  into  a  suitable  clock 
circuit,  in  place  of  the  ordi- 
nary chronograph  pen.  In-  The  Photo-chronograph  (Fargis-Saegmiiller) 


216       The  Observatory  and  its  Instruments 

stead  of  a  star  transit,  or  ordinary,  horizontal  trail  like  this  — 


Ordinary  Star  Trail 

the  plate  when  developed  will  show  this  — 


--H---H 


Interrupted  Star  Trail 

It  is  easy  to  find  the  particular  second  corresponding  to  each  on<- 
of  the  little  broken  trails  on  the  plate,  and  by  usin.?  a  magnifying 
glass  the  fractional  parts  of  seconds  where  the  reticle  lines  cross  the 
trails  can  be  measured  with  accuracy  and  with  almost  no  effect  of  per- 
sonal equation.  In  another  form  of  photo-chronogiaph,  the  plate  is 
stationary,  and  the  armature  actuates  an  occulting  bar,  which  screens 
the  plate  except  for  an  instant  at  the  end  of  each  second.  The  star 
trail  is  then  reduced  to  a  series  of  equidistant  dots. 

The  Meridian  .Circle.  —  The  meridian  circle  is  an  instrument  for 
measuring  right  ascensions  and  declinations  of  heavenly  bodies.  Its 

foundations  are  two  piers  or 
pillars,  in  an  east  and  west  line. 
On  top  of  each  is  a  Y?  or  bear- 
ing, and  in  these  turn  two 
pivots,  accurately  fashioned, 
cylindrical  in  form.  On  top  of 
them  rests  an  accurate  striding 
level.  The  pivots  are  attached 
solidly  to  the  massive  axis 
proper,  this  latter  being  made 
up  of  two  cylinders,  or  in- 
verted cones,  and  a  centrrl 
cube  between  them,  through 
which  passes  the  telesc  pe, 

Meridian  Circle  (>rom  a  Design  by  Landreth)       rigidly    fastened    perpendicular 

to    axis.      On    either    side    of 

the  telescope,  a  finely  divided  circle  is  secured  at  right  angles  to  the 
axis.     Circles,  axis,  telescope,  and  pivots,  then,  all  revolve  roun4  in  the 


The  Equatorial  Coude  2 1 7 

Y's  together,  as  one  solid  piece.  The  delicate  bearings  are  in  part  re- 
lieved of  this  great  weight  by  means  of  counterpoises.  Firmly  attached 
to  the  right  pier  are  microscopes  for  reading  with  high  accuracy  the 
graduation  on  the  rim  of  the  circle.  The  zero  point  of  the  circle  is 
usually  found  by  placing  a  basin  of  mercury  underneath  the  telescope, 
which  is  then  pointed  downward  upon  the  mercury.  When  the  hori- 
zontal lines  in  the  field  of  view  are  seen  to  correspond  exactly  with 
their  images  reflected  from  the  mercury,  the  position  of  the  circle  is  read 
from  the  microscopes ;  and  this  is  the  zero  point,  because  the  line  of 
sight  through  the  telescope  is  then  vertical.  The  operation  of  obtain- 
ing this  zero  point  is  called  '  taking  a  nadir.'  Combining  it  with  the 
latitude  of  the  place  gives  the  circle  reading  for  pole  or  equator,  and 
so  any  star's  declination  may  be  found.  The  meridian  circle  is  often 
called  also  the  transit  circle.  Right  ascensions  are  observed  with 
the  meridian  circle  exactly  as  with  the  transit  instrument  previously 
described. 

The  Equatorial  Coude.  —  A  very  advantageous  and  convenient  combi- 
nation of  refractor  and  reflector  is  the  T-shaped  or  '  elbow  telescope,1 
called  the  equatorial  coudd.  It  was  invented  by  Loewy,  the  present 
director  of  the  Paris  Observatory,  and  is  a  type  of  instrument  well  known 
in  the  observatories  of  France, 
although  there  are  as  yet  none 
in  the  United  States.  The 
chief  advantage  is  that  the 
instrument  itself,  as  shown  in 
the  illustration,  is  nearly  all 
in  open  air,  while  the  observer 
sits  in  a  fixed  position,  as  if 
working  at  a  microscope  on  The  Equatorial  Coude  aoewy) 

a  table.  The  eyepiece,  there- 
fore, is  in  a  room  which  may  be  kept  at  comfortable  temperatures 
in  winter.  The  instrument  can  be  handled  easily  and  rapidly,  and  is 
very  convenient  for  the  attachment  of  spectroscopes  and  cameras.  The 
splendid  lunar  photographs  on  pages  16  and  248  were  taken  with  this 
telescope.  Its  chief  disadvantage  is  loss  of  light  by  reflection  from 
two  plane  mirrors,  set  at  an  angle  of  45°  in  two  cubes  shown  at  the 
lower  end  of  the  polar  axis.  The  object  glass  is  mounted  in  one 
side  of  the  right-hand  cube,  near  the  attendant.  This  cube  with  its 
mirror  and  objective  turns  round  on  an  axis  in  line  with  the  central 
cube,  and  forming  the  declination  axis.  Beneath  the  central  cube  is 
the  lower  pivot  of  the  polar  axis.  The  long  oblique  telescope  tube  is 
itself  the  polar  axis,  and  its  upper  bearing  is  near  the  eyepiece.  A 
powerful  clock  carries  the  whole  instrument  round  to  follow  the  stars, 
and  the  upper  cube  is  counterpoised  by  a  massive  round  weight  at  the 


218       The  Observatory  and  its  Instruments 

lower  end  of  the  declination  axis.  First  cost  of  the  equatorial  coude 
is  about  double  that  of  the  usual  type  of  equatorially  mounted  telescope  ; 
but  the  large  expense  for  a  dome  is  mostly  saved,  as  the  coude  is 
housed  under  a  light  structure  which  rolls  off  on  rails  to  the  position 
shown  in  the  engraving. 

Common  Mistakes  about  Telescopes.  —  Perhaps  the  question  most 
often  asked  the  astronomer  by  persons  uninformed  is,  How  far  can  you 
see  with  your  telescope  ?  Evidently  no  satisfactory  answer  can  be  given, 
for  all  depends  upon  what  one  wants  to  see.  If  terrestrial  distance  is 
meant,  the  large  telescope  does  not  possess  an  advantage  proportionate 
to  its  size.  All  objects  on  the  earth  must  be  observed  through  lower 
strata  of  the  atmosphere,  and  these  regions  are  so  much  disturbed  in 
the  daytime  by  intermingling  of  air  currents,  warm  and  cold,  that 
the  high  magnifying  powers  of  large  telescopes  cannot  be  advanta- 
geously used.  If  celestial  distance  is  meant  by  the  question,  How  far? 
the  answer  can  only  be  inconclusive,  because  the  telescope  enables  us 
to  see  as  far  as  starlight  can  travel.  The  brighter  the  star,  the  greater 
distance  it  can  be  seen,  independently  of  the  telescope.  The  smallest 
glass  will  show  stars  so  far  away  that  light  requires  hundreds  of  years 
to  reach  us  from  them.  The  larger  the  telescope,  the  fainter  the  star  it 
will  show ;  but  it  is  not  known  whether  these  fainter  stars  are  fainter 
because  of  their  greater  distance  or  simply  because  they  are  smaller  or 
less  luminous.  Another  common  question  is,  How  much  does  your 
telescope  magnify?  as  if  it  had  but  one  eyepiece.  Actually  it  will  have 
several,  for  use  according  to  the  condition  of  the  atmosphere  and  the 
character  of  the  object.  A  more  intelligent  question  would  be,  What  is 
the  highest  magnifying  power?  This  will  never  exceed  100  diameters 
to  each  inch  of  aperture  of  the  objective,  and  70  to  the  inch  is  an 
average  maximum.  Even  this,  however,  is  high,  if  advantageous 
magnifying  power  is  meant.  So  unsteady  is  the  atmosphere  in  the 
eastern  half  of  the  United  States  that  magnifying  powers  exceeding 
50  to  the  inch  cannot  often  be  used  to  advantage  in  observing  the 
planets. 

Celestial  Photography.  —  As  soon  as  Daguerre,  in  1839,  had  invented 
photography,  it  was  at  once  seen  that  the  brighter  heavenly  bodies 
might  be  photographed,  because  telescopes  are  used  to  form  images 
of  them  in  exactly  the  same  way  that  the  camera  produces  an  image  of 
a  person,  a  building,  or  a  landscape.  Photography  is  simply  a  process 
of  fixing  the  image.  In  1840  the  moon  was  first  photographed,  in  1850 
a  star,  in  1851  the  sun's  corona,  in  1854  a  solar  eclipse,  in  1872  the 
spectrum  of  a  star,  in  1880  a  nebula,  in  1881  a  comet,  and  in  1891  a 
meteor.  All  these  photographs,  except  the  meteor  and  the  corona,  were 
first  made  in  America.  Continued  improvement  in  processes  of  photog- 
raphy makes  it  possible  to  take  pictures  of  fainter  and  fainter  celestial 


Photographs  of  the  Heavenly  Bodies        219 

bodies,  and  the  larger  telescopes  have  photographed  exceedingly  faint 
stars  which  the  human  eye  has  never  seen  —  perhaps  never  can  see. 
This  is  done  by  exposing  the  sensitive  plate  for  many  hours  to  the 
light  of  such  bodies ;  for,  while  in  about  10  seconds  the  human  eye, 
by  intense  looking,  becomes  weary,  the  action  of  faint  rays  of  light 
upon  the  photographic  plate  is  cumulative,  so  that  the  result  of  several 
hours'  exposure  is  rendered  readily  visible  when  the  plate  is  devel- 
oped. In  this  way,  an  extra  sensitive  dry  plate,  of  the  sort  most  generally 
employed,  will  often  record  many  thousand  telescopic  stars  in  a  region 
of  sky  where  the  naked  eye  can  see  but  one  (page  458).  Nearly  every 
branch  of  astronomical  research  has  been  advanced  by  the  aid  of  pho- 
tography, so  universal  are  its  applications  to  astronomy. 

How  to  take  Photographs  of  the  Heavenly  Bodies.  —  Any  good  tele- 
scope or  camera  may  be  satisfactorily  used  in  taking  photographs  of 
celestial  objects.  Remove  the  eyepiece,  and  substitute  in  its  place  a 
small,  light-tight  plate-holder.  Fasten  it  to  the  tube  temporarily,  so 
that  the  plate  will  be  in  the  focus  of  the  object  glass.  This  point  may 
be  found  by  moving  forth  and  back  a  piece  of  greased  or  paraffin  paper, 
until  the  image  of  the  moon  is  seen  sharply  defined.  Adjust  plate- 
holder  and  finder  so  that  when  an  object  is  in  the  field  of  the  finder, 
it  will  also  be  on  the  center  of  the  plate.  Insert  a  plate  in  this  position, 
and  make  an  exposure  of  about  half  a  second  on  the  moon,  if  within 
two  or  three  days  of  the  '  quarter.'  The  object  glass  should  be  covered 
by  a  cap  or  diaphragm  having  about  three  fifths  the  full  aperture  of  the 
lens.  On  developing,  the  moon's  image  will  be  somewhat  blurred.  In 
part  this  is  because  the  best  focus  for  photographing  is  either  outside  or 
inside  the  visual  focus,  found  by  the  greased  paper.  To  find  the  best 
focus,  move  the  plate-holder  farther  from  the  lens,  first  \  inch,  then  \ 
inch,  then  f  inch,  then  i  inch,  making  at  each  point  an  exposure  of 
the  same  length  as  before.  Compare  the  negatives.  The  true  photo- 
graphic focus  lies  nearest  the  point  where  the  best-defined  picture  was 
taken.  If  desired,  the  process  may  be  repeated  near  this  point,  shift- 
ing the  plate  only  a  few  hundredths  of  an  inch  each  time.  If  the 
pictures  are  more  and  more  blurred  the  farther  the  plate  is  moved  from 
the  lens,  the  focus  for  photography  may  be  inside  the  visual  focus 
first  found,  and  the  plate-holder  should  then  be  moved  in  accordingly, 
making  trials  at  different  points.  When  the  photographic  focus  is 
finally  found,  the  plate-holder  should  be  securely  fastened  to  the  eye- 
piece tube,  or  adapter ;  and  a  mark  made  so  that  it  may  readily  be 
adjusted  to  the  same  spot  whenever  needed  in  the  future.  A  meniscus 
of  suitable  curvature  is  sometimes  attached  in  front  of  the  object  glass, 
to  focus  the  photographic  rays  (about  \  nearer  the  objective).  Also 
E.  C.  Pickering  has  found  that  an  achromatic  objective  with  crown  lens 
properly  figured  can  be  converted  into  a  photographic  telescope  by 


22O       The  Observatory  and  its  Instruments 

reversal  of  the  crown  lens.     In  achromatic  objectives  of  the  new  Jena 
glass,  visual  and  photographic  foci  are  practically  coincident. 

Astronomical  Discoveries  made  by  Photography.  —  The  great  benefit 
to  astronomy  from  the  application  of  photography  in  making  discoveries 
was  first  realized  when,  during  the  total  eclipse  of  1882  in  Egypt,  the 
photographic  plate  discerned  a  comet  close  to  the  sun  (page  301).  But 
interest  was  intensified  when  a  hazy  mass  of  light  was  seen  to  surround 
the  star  Maia  of  the  Pleiades,  on  a  plate  exposed  for  about  an  hour  to 
that  group  of  stars  in  November,  1885.  This  astronomical  discovery 
by  means  of  photography  was  soon  after  verified'  by  the  3O-inch  tele- 
scope at  Pulkowa,  Russia.  Many  other  nebulae,  both  large  and  small, 
have  since  been  discovered  by  photography,  some  of  which  have  been 
verified  by  the  eye.  By  photographing  spectra  of  stars,  peculiarities  of 
constitution  have  been  immediately  revealed  which  the  eye  had  long 
failed  to  discover  directly  (page  444) .  Several  new  double  stars  have 
been  found  in  this  way,  and  important  discoveries  as  to  classification 
of  stars  have  been  made  from  critical  study  of  stellar  spectrum  photo- 
graphs (page  444).  Long  exposures  of  comets  have  brought  to  light 
certain  details  of  structure  which  the  eye  has  failed  to  detect  (page 
406).  In  discovering  minor  planets,  photography  has,  since  1890,  been 
of  constant  assistance  because  of  ease  and  accuracy  in  mapping  fixed 
stars  in  the  neighborhood  of  these  minute  objects.  It  is  about  20  times 
easier  to  find  a  small  planet  on  a  photographic  plate  than  by  the  former 
method  of  mapping  the  sky  optically.  But  discoveries  in  solar  physics 
by  means  of  photography  are  most  important  of  all,  for  it  has  been 
found  that  the  faculae,  or  white  spots,  extend  all  the  way  across  the  sun's 
disk  in  about  the  same  zones  that  spots  do  (page  269)  ;  and  complete 
photographic  records  of  the  sun's  chromosphere  and  prominences  are 
now  made  every  day  by  means  of  radiations  to  which  photographic 
plates  are  very  sensitive,  but  which  our  eyes  unaided  are  powerless  to 
see.  Lunar  photographs,  too,  are  thought  by  some  astronomers  to  have 
revealed  minute  details  which  the  eye  has  failed  to  detect. 

We  now  turn  to  a  consideration  of  present  knowledge  of 
our  satellite,  and  of  the  other  and  more  remote  orbs  of 
heaven,  as  disclosed  by  the  instruments  of  which  we  have 
just  learned. 


CHAPTER    X 

THE   MOON 

THE  moon  was  the  subject  of  the  most  ancient  astro- 
nomical observations,  for  elementary  study  of  her 
motion  was  found  both  easy  and  useful.     The  wax- 
ing and  waning  phases,  too,  must  have  excited  the  curi- 
osity of   early  peoples,  who  were  unacquainted  with  the 
true  explanation  of  even  so  elemental  a  phenomenon.     Let 
us  now  watch  our  satellite  from  night  to  night.     A  few 
evenings'  observations  show  how  easy  it  is  to  find  out  the 
general  facts  of  her  motion  around  us. 

To  observe  the  Moon's  Motion.  —  The  September  new  moon,  first 
becoming  visible  in  the  southwest,  will,  in  about  five  days,  reach  the 
farthest  declination  south,  and  culminate  near  the  lowest  point  on  the 
meridian.  Thenceforward,  for  about  a  fortnight,  she  will  be  farther  and 
farther  north  each  night,  journeying  at  the  same  time  eastward,  and  in 
a  general  way  following  the  ecliptic.  During  the  subsequent  fortnight, 
the  moon  will  be  traveling  southward,  always  within  the  zodiac ;  and 
in  a  little  less  than  a  month,  will  have  returned  very  nearly  to  the 
point  where  we  first  began  to  observe.  And  so  on,  throughout  all 
time,  with  a  regularity  which  became  useful  to  the  ancients  as  a  meas- 
ure of  time  ;  for  our  month  took  its  origin  from  the  moon^  period  round 
the  earth.  But  her  motion  is  even  more  useful  to  the  modern  world, 
because  employed  by  navigators  on  long  voyages  in  finding  the  position 
of  ships.  So  important  is  the  moon  in  this  relation  that  the  lives  of 
many  great  mathematical  astronomers  have  been  almost  wholly  devoted 
to  the  study  of  her  motion.  Americans  prominent  in  this  line  of  re- 
search are  Nevvcomb  and  G.  W.  Hill.  As  soon  as  the  new  moon  can 
first  be  seen  in  the  western  sky,  make  a  long,  narrow  chart  of  the 
brighter  stars  to  the  east  within  the  zodiac  as  on  the  next  page.  A  line 
.drawn  eastward  from  the  moon,  perpendicular  to  the  line  joining  the 

221 


222 


The  Moon 


\ 


NEW  CRESCENT 
MOON 


FIRST  QUARTER 


GIBBOUS  MOON 
BEFORE  FULL 


horns  of  the  crescent,  called  cusps,  will  show  this  direction  accurately 
enough.  Then  plot  the  moon  among  the  stars  on  the  chart  each  clear 
^  night.  Also  draw  the  phase  asv 

^          accurately  as  possible.     It  is  bet- 
— °          ter  to  chart  the  position  about  half 
/  .  an  hour  later  each  night.      This 

^          simple  series  of  observations  may 

continue  nearly  three  weeks,  if 
desired.  Much  will  be  learned 
from  it,  —  position  of  the  ecliptic  ; 
progressive  phases  of  the  moon ; 

^    %>     the  amount  of  motion  each  day 

^      (about    her    own    breadth    every 
-j    "^     hour,  or  13°  in  a  day)  ;  and  if  a 
Q     telescope  is  used,  the  observer  will 
d    |     occasionally  be  rewarded  by  the 
— 3  ^      opportunity  of  watching  the  moon 
js     pass  over,  or  occult,  a  star.     Dis- 

1j  a      appearance  of  a  star  at  the  moon's 

•5      dark  limb  is  the  most   nearly  in- 
_5    c°     stantaneous    of    all    natural   phe- 
— 3    E      nomena. 


FULL  MOON 


GIBBOUS  MOON 
AFTER  FULL 


THIRD  OR  LAST 
QUARTER 


OLD  CRESCENT 
MOON 


o 


The  Terminator.  —  Ob- 
serve the  slender  moon  in 
the  west,  as  soon  as  she  can 
be  seen  in  a  dark  sky.  The 
inside  edge  of  the  bright 
crescent,  or  the  line  where 
the  lucid  part  of  the  moon 
joins  on  the  dark  or  faintly 
illuminated  portion,  is  called 
the  terminator;  and  its  gen- 
eral curvature  is  always  a 
half  ellipse,  never  a  semi- 
circle. 

The  moon's  terminator  is  ellip- 
tical in  figure  because  it  is  a  semi- 
circle seen  obliquely.  Any  circle 
not  seen  perpendicularly  seems  to 


The  Moons  Phases 


223 


be  shaped  like  an  ellipse ;  and  the  more  obliquely  it  is  seen,  the  more 
the  ellipse  appears  elongate  or  drawn  out.  When  turning  a  curve  on 
your  bicycle,  observe  the  changing  figure  of  the  shadows  of  its  wheels 
cast  by  the  sun.  Owing  to  mountains  on  the  lunar  surface,  the  actual 
terminator,  if  examined  with  a  telescope,  is  always  a  broken,  jagged 
line.  This  is  because  sunlight  falls  obliquely  across  the  rough  surface, 
and  all  its  irregularities  are  accentuated  as  if  magnified  —  like  pebbles 
and  ruts  in  the  road,  at  a  considerable  distance  from  an  arc  light. 


FIRST 
'QUARTER 


/EARTH) 


THIRD     (__ 
UARTER W 


THIRD 
QUARTER' 


V         £"-        W 

MOON 
Phases  as  seen  from  above  Moon's  Orbit 


o 


. 


o 


MOON 

Corresponding  Phases  from  the  Earth 


Explaining  Phases  of  the  Moon 

The  Moon's  Phases The  moon's  phases  afforded  trav- 
elers and  shepherds  the  first  measure  of  time.  When  two 
or  three  days  after  new  moon  our  satellite  is  first  seen  in 
the  western  sky,  her  form  is  a  crescent,  convex  westward 
or  toward  the  sun,  with  the  horns,  or  cusps  turned  toward 
the  east.  Three  or  four  days  later  the  slender  crescent 
having  grown  thicker  and  thicker,  and  the  terminator  less 
and  less  curved,  the  moon  has  reached  quadrature,  or  first 
quarter,  and  her  shape  is  that  of  a  half  circle.  The  termi- 
nator is  then  a  straight  line,  the  diameter  of  this  circle. 
Passing  beyond  quadrature,  the  terminator  begins  to  curve 


224  The  Moon 

in  the  opposite  direction,  making  the  moon  appear  shaped 
somewhat  like  a  football,  with  one  side  circular  and  the 
other  elliptical.  The  eastern  edge  is  the  elliptical  one, 
and  is  still  called  the  terminator.  Gradually  its  curva- 
ture increases,  the  apparent  disk  of  the  moon  growing 
larger  and  larger,  until,  about  a  week  after  first  quarter, 
the  phase  called  full  moon  is  reached.  This  oblong 
moon,  between  first  quarter  and  full,  is  called  gibbous 
moon.  From  full  moon  onward  for  a  week,  our  satellite 
is  again  gibbous  in  form,  but  the  terminator  has  now 
changed  to  the  west  side  of  the  lunar  disk,  instead  of 
the  eastern.  Then  quadrature  is  reached,  and  the  moon 
is  again  a  half  circle,  but  turned  toward  the  east,  not  the 
west.  This  phase  is  known  as  third,  or  last  quarter.  On- 
ward another  week  to  new  moon,  the  figure  is  again  cres- 
cent, but  curving  eastward  or  toward  the  sun,  and  the 
horns  pointing  toward  the  west.  All  the  figures  previously 
shown  —  crescent,  quarter,  gibbous,  and  full  —  represent 
phases  of  the  moon. 

Cause  of  the  Moon's  Phases.  —  Our  satellite  is  herself  a 
dark,  opaque  body.  But  the  half  turned  toward  the  sun  is 
always  bright,  as  in  the  last  figure ;  the  opposite  half  is 
unillumined,  and  therefore  usually  invisible.  While  the 
moon  is  going  once  completely  round  the  earth,  different 
regions  of  this  illuminated  half  of  our  satellite  are  turned 
toward  us;  and  this  is  the  cause  of  phases  of  the  moon. 

To  illustrate  in  simple  fashion :  accurately  remove  the  peel  from  the 
half  of  an  orange.  Let  a  lamp  in  one  corner  of  a  room  otherwise  dark 
represent  the  sun.  Standing  as  far  as  convenient  from  the  lamp,  let 
the  head  represent  the  earth,  and  the  orange  held  at  arm's  length, 
the  moon.  Turn  the  white  half  of  the  orange  toward  the  lamp.  Now 
turn  slowly  round  toward  the  left,  at  the  same  time  turning  the  orange 
on  its  vertical  axis,  being  careful  always  to  keep  the  peeled  side  of  the 
orange  squarely  facing  the  lamp.  While  turning  round,  keep  the  eye 
constantly  fixed  on  the  white  half  of  the  orange,  and  its  changing 


Earth  Shine 


225 


shape  will  represent  all  the  moon's  successive  phases :  new  moon  when 
orange  is  between  eye  and  lamp  ;  first  quarter  (half  moon)  when  orange 
is  at  the  left  of  lamp  and 
at  a  right  angle  from  it ; 
full  moon  when  orange  is 
directly  opposite  lamp ; 
last  quarter,  orange  oppo- 
site its  position  at  first 
quarter.  When  the  orange 

shows  a  slender  crescent,  •, '   |H  4Rl  ''"til 

at  either  old  or  new  moon, 
shield  the  eye  from  direct 
light  of  lamp.  Again  re- 
peat the  experiment,  and 
watch  the  gradually  curv- 
ing terminator  from  phase 
to  phase.  The  unpeeled 
half  of  the  orange,  too, 
represents  very  well  the 
moon's  ashy  light,  or 
earth  shine  on  the  moon, 
when  a  narrow  crescent. 

Earth  Shine.  —  The 
nights  on  the  moon 
are  brightened  by  re- 
flected light  from  the 
neighborly  earth,  and 
our  shining  is  equal  to  more  than  a  dozen  full  moons. 
This  light  it  is  that  makes  the  faint  appearance  on  the 
moon,  as  of  a  dark  globe  filling  the  slender  crescent  of  the 
new  moon,  causing  a  phenomenon  called  '  the  old  moon 
in  the  new  moon's  arms.'  Similarly  with  the  decrescent 
old  moon. 

The  copper  color  of  the  earth-illumined  portion  is  explained  by  the 
fact  that  the  earth  light  has  passed  twice  through  our  atmosphere  before 
reaching  the  moon,  and  by  a  peculiar  property  of  the  atmosphere,  it 
absorbs  bluish  rays  and  allows  reddish  ones  to  pass.  Always  the 
phase  of  this  portion  of  the  moon  is  the  supplement  of  the  phase  of  the 
bright  portion.  Also  its  figure  is  exactly  that  which  the  bright  earth 
TODD'S  ASTRON.  — 15 


Illustrating  the  Moon's  Progressive  Phases 


226  The  Moon 

would  appear  to  have,  if  seen  from  the  moon.     When  our  satellite  is 
crescent  or  decrescent  to  us,  the  earth  shows  gibbous  to  the  moon. 

North  and  South  Motion  of  the  Moon. — Just  as  the  sun 
has  a  north  and  south  motion  in  a  period  of  a  year,  so  the 
moon  has  a  similar  motion  in  a  period  of  about  a  month ; 
for  she  follows  in  a  general  way  the  direction  of  the  ecliptic. 
Every  one  has  observed  that  midsummer  full  moons  always 
cross  the  meridian  low  down,  and  that  the  full  moons  of 
midwinter  always  culminate  high. 

'The  reason  is  that  the  full  moon  is  always  about  180  degrees  from 
the  sun.  Similarly  midwinter  crescent  moons,  whether  old  or  new,  are 
always  low  on  the  meridian,  and  crescent  moons  of  midsummer  always 
high.  So  when  in  summer  you  see  in  early  evening  the  new  moon  in 
the  northwest,  you  know  that  in  winter  the  old  moon's  slender  crescent 
must  be  looked  for  in  the  early  morning  in  the  southeast.  Remember 
that  our  satellite  from  new  to  full  is  always  east  of  the  sun.  And 
whether  the  moon  in  this  part  of  its  lunation  is  to  be  found  north  or 
south  of  the  sun  will  depend  upon  the  season.  For  example,  the  moon 
at  first  quarter  will  run  highest  in  March,  because  the  sun  is  then  at  the 
vernal  equinox,  and  the  moon  at  the  summer  solstice.  For  a  like  reason 
the  first-quarter  moon  which  runs  lowest  on  the  meridian  will  <  full '  in 
the  month  of  September. 

The  Moon  rises  about  Fifty  Minutes  later  Each  Day.  — 
Her  own  motion  eastward  among  the  stars,  about  13°  every 
day,  causes  this  delay.  As  our  ordinary  time  is  derived 
from  the  sun  (itself  not  stationary  among  the  stars,  but 
also  moving  eastward  every  day  about  twice  its  own 
breadth,  or  i°),  therefore  the  eastward  gain  of  the  moon 
on  the  sun  is  about  12°.  Now  suppose  the  moon  on 
the  eastern  horizon  at  7  o'clock  this  evening;  then,  to- 
morrow evening  at  7,  it  is  clear  that  if  her  orbit  stood  ver- 
tical, she  would  be  12°  below  the  horizon,  because  in  that 
part  of  the  sky  the  direction  east  is  downward.  But  by 
the  earth's  turning  round  on  its  axis,  the  stars  come  above 
the  eastern  horizon  at  the  rate  of  1°  in  four  minutes  of 
time ;  therefore  to-morrow  evening  the  moon  will  rise  at 


Harvest  and  Hunters  Moon  227 

about  50  minutes  after  7.     And  so  on,  about  50  minutes 
later  on  the  average  each  night. 

Variation  from  Night  to  Night.  —  Consult  the  almanac 
again.  In  it  are  printed  the  times  of  moonrise  for  every 
day.  Wait  until  full  moon,  and  verify  these  times  for  a 
few  successive  days,  if  the  eastern  horizon  permits  an  un- 
obstructed view.  Having  found  the  almanac  reliable,  at 
least  within  the  limits  of  error  of  observation,  we  may  use 
its  calculations  to  advantage  for  other  days  of  the  year; 
for  on  many  of  these  it  will  not  be  possible  to  watch 
the  moon  come  up,  because  she  rises  in  the  daytime.  The 
difference  of  rising  (or  of  setting)  from  one  day  to  another 
may  sometimes  be  less  than  half  an  hour,  and  again  about 
a  fortnight  later,  a  full  hour  and  a  quarter. 

There  are  two  reasons  for  this :  (i)  The  apparent  monthly  path  of 
the  moon  lies  at  an  angle  to  the  horizon  which  is  continually  changing ; 
when  the  angle  is  greatest,  near  the  autumnal  equinox,  a  day's  east- 
ward motion  of  our  satellite  will  evidently  carry  her  farthest  below  the 
eastern  horizon.  (2)  The  moon's  path  around  us  is  elliptical,  not  circu- 
lar, and  the  earth  is  not  at  the  center  of  the  ellipse,  but  at  its  focus, 
so  that  earth  and  moon  are  nearest  together  and  farthest  apart  alter- 
nately at  intervals  of  about  two  weeks.  By  the  laws  of  motion  in  such 
an  orbit,  the  moon  travels  her  greatest  distance  eastward  in  a  day 
when  nearest  the  earth  (perigee)  ;  and  her  least  distance  eastward  when 
farthest  from  the  earth  (apogee) .  And  this  change  in  speed  of  the 
moon's  motion  also  affects  the  time  of  rising  and  setting. 

Harvest  and  Hunter's  Moon.  —  Every  month  the  moon 
goes  through  all  the  changes  in  the  amount  of  delay  in  her 
rising,  from  the  smallest  to  the  largest.  But  ordinarily 
these  are  not  taken  especial  account  of,  unless  at  the  time 
when  least  retardation  happens  to  coincide  nearly  with 
time  of  full  moon.  Now  the  epoch  of  least  retardation 
occurs  when  the  moon  is  near  the  vernal  equinox,  be- 
cause there  the  moon's  path  makes  the  smallest  angle  with 
the  eastern  horizon.  And  as  sun  and  full  moon  must  be 


228  The  Moon 

in  opposite  parts  of  the  sky,  autumn  is  the  season  when 
full  moon  and  least  retardations  come  together. 

The  daily  advance  of  the  moon  along  the  September  ecliptic  is  from 
i  to  2,  and  from  2  to  3.  In  March  the  same  amount  of  eastward 
advance,  from  I  to  2',  and  from  2'  to  3',  brings  the  moon  much  farther 
below  the  horizon,  and  therefore  retards  the  time  of  rising  by  the  greatest 
amount,  as  the  dotted  lines  drawn  parallel  to  the  equator  show.  Simi- 
larly the  positions  at  2  and  3  give  the  least  delay ;  and  this  September 
full  moon,  rising  less  than  a  half  hour  later  each  evening,  is  called  the 
harvest  moon.  A  month  later  the  retardation  is  still  near  its  least 
amount  for  a  like  reason  ;  and  the  October  full  moon  is  called  the 
hunter's  moon.  Approaching  the  tropics,  where  equator  and  ecliptic 
stand  more  nearly  vertical  to  the  horizon,  it  is  clear  that  the  phe- 
nomena of  the  harvest  moon  become  much  less  pronounced. 


EAST       HORIZON 

/>-^/1     / 


.&V/      ->--~//i    X 

^/j/:/ 


.'2'     s'* 

/'./• 


f 

Circumstances  of  Harvest  Moon 


The  Moon's  Period  of  Revolution.  —  The  moon  revolves 
completely  round  the  starry  heavens  in  27^  days  (or  more 
exactly  27  d.  7  h.  43  m.  1 1.5  s.).  This  is  called  the  sidereal 
period  of  the  moon,  because  it  is  the  time  elapsed  while  she 
is  traveling  from  a  given  star  eastward  round  to  the  same 
star  again.  This  motion  of  the  moon  must  be  kept  en- 
tirely distinct  from  the  apparent  diurnal  motion,  or  simple 
rising  in  the  east  and  setting  in  the  west ;  for  the  latter 
is  a  motion  of  which  all  the  stars  partake,  and  is  wholly 


The  Moons  Synodic  Period 


229 


due  to  the  earth's  revolution  eastward  upon  its  axis.  But 
our  satellite's  own  motion  along  her  path  round  the  earth  is 
in  the  opposite  direction ;  that  is,  from  west  toward  east. 
A  rough  value  for  the  sidereal  period  is  easy  to  determine. 

Select  any  bright  star  (not  a  planet)  near  the  moon ;  for  example, 
Alpha  Scorpii,  on  3Oth  September,  1897,  at  about  7  P.M.,  Eastern 
Standard  time.  The  star  and  the  center  of  the  moon  are  then  nearly 
on  the  same  hour  circle  ;  that  is,  their  right  ascensions  are  about  equal. 
The  fojlowing  month  watch  for  the  moon's  return  to  the  same  star ;  on 
the  evening  of  27th  October,  at  6  o'clock,  the  moon  has  not  yet 
reached  the  star,  but  is  about  nine  times  her  own  breadth  west  of  the 
star.  So  star  and  moon  are  together  about  three  in  the  morning  of 
28th  October.  The  difference,  then,  or  27  d.  8h.,  although  a  crude 
verification  of  the  sidereal  period,  has  been  rightly  obtained. 

The  Moon's  Synodic  Period.  —  Let  sun  and  moon  appear  together 
in  the  sky  as  seen  from  the  earth  at  £",  sun  being  at  S,  and  moon  at  Mr 
While  earth  is  trav- 
eling eastward  round 
the  sun  in  the  direc- 
tion of  the  large  ar- 
row, moon  is  all  the 
time  going  round 
earth  in  the  direc- 
tion M^M^  indicated 
by  the  small  arrow. 
When  earth  has 
reached  E ',  moon  is 
at  mv  and  her  side- 
real period  is  then 
complete,  because 
m^E!  is  parallel  to 
M^E.  But  the  sun 
is  in  the  direction 

E'S.  So  the  moon  must  move  on  still  further,  making  the  period  rela- 
tively to  the  sun  longer  than  her  sidereal  period,  just  as  the  sidereal  day- 
is  shorter  than  the  solar  day.  In  round  numbers,  the  sun's  apparent 
motion,  while'the  moon  has  been  traveling  round  us,  amounts  to  about 
30° ;  therefore  the  moon  must  travel  eastward  by  this  amount,  or  nearly 
2\  days  of  her  own  motion,  in  order  to  overtake  the  sun. 

The  period  of  the  moon's  motion  round  the  earth  rela- 
tively to  the  sun  is  called  the  synodic  period.  It  is 


Synodic  Period  exceeds  Sidereal  Period 


230  The  Moon 

days  in  duration,  or  accurately  29  d.  12  h.  44m.  2.75.,  as 
found  by  astronomers  from  several  thousand  revolutions 
of  the  moon.  It  is  an  average  or  mean  period,  depending 
upon  the  mean  motion  of  the  sun  and  the  mean  motion  of 
the  moon  ;  for  we  shall  soon  find  that  our  satellite  travels 
round  us  with  a  speed  far  from  uniform,  just  as  we  found 
our  own  motion  round  the  sun  to  be  variable.  The  synodic 
period  may  be  roughly  verified  by  observing  the  times  of 
a  given  phase  of  the  moon  with  about  a  year's  interval 
between  them,  and  dividing  by  the  whole  number  of  luna- 
tions. For  example,  on  2d  October,  1897,  at  about  nine  in 
the  evening,  the  terminator  is  judged  to  be  straight,  and  it 
is  first  quarter.  Similarly,  on  22d  September,  1898,  at  6 
o'clock  P.M.  Divide  the  entire  interval  of  354.9  days  by 
12,  the  number  of  intervening  lunations,  and  the  result  is 
29.58  d.,  only  one  hour  in  error. 

The  Lunation.  —  The  term  lunation  is  often  used  with 
the  same  signification  as  the  synodic  period.  More  prop- 
erly the  lunation  is  the  period  elapsing  from  one  new 
moon  to  the  next.  Its  value  cannot  be  found  directly  by 
observation,  but  only  from  calculation,  because  at  new 
moon  the  dark  half  of  our  satellite  is  turned  toward  us, 
and  the  disk  is  merged  in  the  background  of  atmosphere 
strongly  illuminated  by  the  sun.  Take  from  any  almanac 
the  difference  between  the  times  of  adjacent  new  moons 
at  different  times  of  the  year.  Some  of  these  will  be 
longer  and  some  shorter  by  several  hours  than  the  synodic 
period.  These  differences  are  mainly  due  to  (a)  the  sun's 
varying  motion  along  the  ecliptic,  and  (b)  the  moon's 
varying  motion  in  her  path  round  the  earth. 

The  Moon's  Apparent  Orbit.  —  So  far  the  moon's  motion 
has  been  accurately  enough  described  by  saying  that  its 
path  coincides  with  the  ecliptic.  But  closer  observation 
will  soon  show  that,  twice  each  month,  our  satellite  deviates 


The  Moons  Apparent  Orbit 


231 


from  the  ecliptic  by  10  times  her  own  breadth.  This  angle, 
more  accurately  5°  8'  40",  is  the  inclination  of  the  moon's 
orbit  to  the  ecliptic,  and  it  varies  scarcely  at  all.  Just  as 
ecliptic  and  equator  cross  each  other  at  two  points  180° 
apart,  called  the  equinoxes,  so  the  moon's  path  and  the 
ecliptic  intersect  at  two  opposite  points,  called  nodes  of 
the  moon's  orbit,  or  more  simply  the  moon's  nodes. 


Illustrating  Inclination  and  Nodes  of  Lunar  Orbit 

In  the  figure  they  are  represented  at  a  and  b,  as  coincident  with  the 
equinoxes,  T  and  =£=.  That,  however,  is  their  position  for  an  instant 
only  ;  for  they  move  constantly  westward  just  as  the  equinoxes  do,  only 
very  much  more  rapidly.  During  the  time  consumed  by  our  satellite 
in  traveling  once  around  us,  the  moon's  nodes  travel  backward  more 
than  twice  the  moon's  breadth;  so  that  in  i8£  years  the  nodes  them- 
selves travel  completely  round  the  ecliptic,  and  return  to  their  former 
position.  When  journeying  from  south  to  north  of  the  ecliptic,  as  from 
d  to  c,  in  the  direction  indicated  by  the  arrow,  the  moon  passes  her 
ascending  node,  at  a.  And  when  going  from  c  to  d,  she  passes  her 
descending  node  at  b.  When  the  inclination  of  the  moon's  orbit  is 


232 


The  Moon 


NEWAMOON 


added  to  the  obliquity  of  the  ecliptic,  our  satellite  moves  in  the  plane 
acbd,  in  the  direction  of  the  arrows  ;  when  the  inclination  is  subtracted, 
she  moves  in  the  plane  agbf.  In  both  cases  the  nodes  coincide  with  the 
equinoxes ;  but  in  the  latter  the  ascending  node  has  moved  round  to  b, 
and  the  descending  node  to  a.  Extreme  range  of  moon's  declination 
is  from  28°. 6  north  to  28°. 6  south. 

Cardinal  Points  of  the  Moon's  Orbit.  —  When  our  satel- 
lite comes  between  earth  and  sun,  as  at  new  moon,  she  is 
said  to  be  in  conjunction ;  at  the  oppo- 
site part  of  her  orbit,  with  sun  and  moon 
on  opposite  sides  of  the  earth,  as  at  full 
moon,  she  is  said  to  be  in  opposition. 
Both  conjunction  and  opposition  are 
often  called  syzygy.  Halfway  between 
the  syzygies  are  the  two  points  called 
quadrature.  At  quadrature  the  differ- 
ence of  longitude  between  sun  and  moon 
is  90°  ;  at  the  syzygies,  this  difference  is 
,OON  alternately  o°  and  1 80°.  The  term  syzygy 
is  derived  from  the  Greek  word  meaning 
a  yoke,  and  is  applied  to  these  two  rela- 
tions of  sun,  earth,  and  moon,  when  all 
these  bodies  are  in  line  in  space  —  or 
nearly  so. 

True  Shape  of  the  Moon's  Orbit  in  Space.  —  If 
the  earth  did  not  move,  the  moon's  orbit  in  space 
would  be  nearly  circular.  But  during  the  month 
consumed  by  the  moon  in  going  once  around  us, 
we  move  eastward  about  T^  of  an  entire  circum- 
ference, or  30°.  The  moon's  orbital  motion  is 
relatively  slow,  the  earth's  relatively  rapid ;  and 
on  this  account  the  moon  winds  in  and  out,  along 
our  yearly  path  round  the  sun.  As  that  illumi- 
nating body  is  about  400  times  more  distant  than  the  moon,  the  true 
shape  of  the  lunar  orbit  cannot  be  shown  in  a  diagram  of  reasonable 
size.  But  a  small  portion  of  the  orbit  can  be  satisfactorily  shown,  as 
above ;  and  it  readily  appears  that  the  moon's  real  path  in  space  is 
always  concave  to  the  sun. 


NEW/MOON 


Orbit  Concave  to  Sun 
even  at  New  Moon 


Distance  of  the  Moon  233 

Form  of  the  Moon's  Orbit  round  the  Earth.  —  In    the 

case  of  sun  and  earth,  we  found  that  the  shape  of  our 
yearly  path  round  him  is  an  ellipse,  without  knowing  any- 
thing about  our  distance  from  him.  In  like  manner  we 
can  find  the  form  of  the  moon's  monthly  orbit  round  the 
earth.  That  also  is  an  ellipse. 

By  measuring  the  moon's  diameter  in  all  parts  of  her  orbit,  we  shall 
find  variations  which  can  be  due  only  to  the  changing  distance  of  our 
satellite  from  us.  The  two  circles  adjacent 
correspond  to  extremes  of  this  variation  :  the 
moon  when  nearest  to  us,  is  said  to  be  at 
perigee,  and  the  outer  circle  represents  its 
apparent  size.  About  a  fortnight  later,  on 
arrival  at  greatest  distance,  called  apogee,  the 
moon's  apparent  size  will  have  shrunk  to  the 
inner  dotted  circle.  Evidently  the  variation 
of  apparent  diameter  is  much  greater  than 
that  of  the  sun ;  therefore  the  moon's  path 
is  a  more  elongated  ellipse. than  the  earth's. 
We  saw  that  the  eccentricity  of  the  earth's 
orbit  is  ^ :  that  of  the  moon's  orbit  is  TV  So  great  is  this  variation 
in  distance  of  our  satellite  that  full  moons  occurring  near  perigee  are 
noticeably  brighter  than  those  near  apogee.  While  at  new  moon,  as 
we  shall  see  in  Chapter  xn,  this  change  of  the  moon's  apparent  diam- 
eter happens  to  be  very  significant ;  for  it  produces  different  types  of 
eclipses  of  the  sun. 

Distance  of  the  Moon.  —  Of  all  celestial  bodies,  excepting 
meteors  and  an  occasional  comet,  the  nearest  to  us  is  the 
moon.  Astronomically  speaking,  and  relatively,  the  moon 
is  very  near,  and  yet  her  distance  is  too  great  to  be  appre- 
hended by  reference  to  any  terrestrial  standard.  As  her 
orbit  is  elliptical  instead  of  circular,  and  as  the  earth  is 
situated  in  one  of  the  foci  of  the  ellipse,  the  average  or 
mean  distance  of  the  moon's  center  from  the  center  of  our 
globe  is  239,000  miles. 

If  the  New  York-Chicago  limited  express  could  travel  from  the  earth 
to  the  moon,  and  should  start  on  New  Year's,  although  it  might  run 


234 


The  Moon 


day  and  night,  it  would  not  reach  the  moon  till  about  the  ist  of  Sep- 
tember. Recalling  definitions  of  the  ellipse  previously  given,  it  will  be 
remembered  that  the  mean  distance  is  not  the  half  sum  of  the  greatest 
and  least  distances,  but  the  mean  of  the  distances  at  all  points  of  the 
orbit.  Also  it  is  equal  to  half  the  major  axis  of  the  orbit.  But  in 
traveling  round  the  earth,  our  satellite  is  not  free  to  pursue  a  path 
which  is  a  true  ellipse,  for  the  attraction  of  other  bodies,  in  particular 
the  sun,  pulls  her  away  from  that  path.  So  the  moon's  center  sometimes 
recedes  to  a  distance  of  253,000  miles,  and  approaches  as  near  as 
221,000  miles. 

What  is  Parallax  ?  —  The  moon's  distance  is  found  by 
measuring  the  parallax.  Parallax  is  change  in  apparent 
direction  of  a  body  due  to  change  of  the  point  of  observa- 
tion. It  is  by  no  means  so  puzzling  as  it  may  look. 


Parallax  decreases  as  Distance  increases 

Place  a  yardstick  on  its  edge  at  the  farther  side  of  a  table,  as  shown. 
Set  up  a  pin,  a  nail,  and  a  screw,  at  convenient  intervals ;  the  nail  at 
twice,  and  the  screw  at  three  times,  the  distance  of  the  pin  from  the 
notch  in  the  card  between  the  eyes.  It  is  better  if  notch,  pin,  nail,  and 
screw  are  in  a  straight  line  nearly  at  right  angles  to  the  yardstick  at  its 
middle  point.  First,  from  the  aperture  in  the  card  at  a,  observe  and 
set  down  in  a  horizontal  line  the  readings  of  pin,  nail,  and  screw,  as 
projected  against  the  rule ;  then  repeat  the  observation  from  £,  in  the 
same  order,  setting  down  readings  in  line  underneath.  Screw,  nail,  and 
pin  all  seem  to  change  their  direction  as  seen  from  the  two  apertures. 
This  apparent  change  of  direction  is  parallax ;  it  is  the  angle  formed 
at  the  object  by  lines  drawn  from  it  to  each  eye.  Now  take  the  differ- 
ences of  the  pairs  of  readings  as  they  stand :  the  difference  of  the  pin 
readings  is  twice  that  of  the  nail  readings,  and  three  times  that  of  the 


Moons  Parallax  at  Different  Altitudes    235 

screw  readings.  Parallax,  then,  is  less,  the  farther  an  object  is  removed 
from  the  base,  or  line  joining  the  two  observation  points.  And  con- 
sidering these  points  fixed,  we  reach  the  general  law  that  — 

The  parallax  of  an  object  decreases  as  its  perpendicular 
distance  from  tJie  base  of  observation  increases. 

The  Moon's  Equatorial  Parallax.  —  In  measuring  celestial 
distances,  obviously  it  is  for  the  interest  and  convenience 


Size  and  Distance  of  Earth  and  Moon  in  True  Proportion 

of  all  astronomers  to  agree  upon  some  standard  by  which 
to  measure  and  indicate  parallaxes.  Such  a  standard  line 
has  been  universally  adopted ;  it  is  the  radius  of  the  earth 
at  the  equator.  The  moon's  parallax,  then,  is  the  angle  at 
the  center  of  that  body  subtended  by  the  equatorial  radius 
of  the  earth.  This 
constant  of  lunar 
parallax  is  nearly  a 
degree  in  amount 
(57'  2").  It  means 
that  an  astronomer, 
if  he  could  take  his 
telescope  to  the 
moon  and  there 
measure  the  earth, 
would  find  its  equa- 
tor to  fill  twice  the 
angle  of  the  moon's 

equatorial    parallax  ;  Parallax  increases  with  Zenith  Distance 

that    is,   the    earth 

would  be  i°  54'  m  diameter  —  an   angle  correctly  repre- 
sented in  the  slim  figure  near  the  top  of  the  page. 

Moon's  Parallax  at  Different  Altitudes. — Whatever  the 


236  The  Moon 

latitude  of  the  place,  the  moon's  parallax  is  the  angle 
filled  by  the  radius  of  the  earth  at  that  place,  as  seen 
from  the  moon.  When  moon  is  in  horizon,  that  radius 
AC  (preceding  diagram)  is  perpendicular  to  the  horizon 
AB,  and  the  parallax  AMC  is  consequently  a  maximum, 
called  the  horizontal  parallax.  Higher  up,  as  at  M1 ,  change 
in  apparent  direction  of  the  moon,  as  seen  from  A  and  C, 
is  less;  that  is,  the  parallax  is  less.  With  the  moon  at 
M",  in  the  zenith,  the  parallax  becomes  zero,  because 
the  direction  of  M"  is  the  same,  whether  viewed  from  A 
or  C.  Thus  we  derive  the  important  generalization,  true  for 
sun  and  planets  as  well  as  moon  :  For  a  heavenly  body  at  a 
given  distance  from  the  earths  center  parallax  increases 
with  the  zenith  distance. 

Parallax  lessens  the  Altitude.  —  True  altitude  of  the 
moon  and  other  bodies  is  measured  upward  from  the  ra- 
tional horizon  to  the  center  of  the  body.  In  the  diagram 
on  the  previous  page,  these  altitudes  are  HCM,  HCM', 
and  HCM" .  But  as  seen  from  the  point  of  observation 
A,  the  moon's  apparent  altitudes  are  o°  at  B,  BAM1 ,  and 
BAM".  It  is  clear  that  these  altitudes  must  always  be  less 
than  the  true  altitudes,  except  when  moon  is  in  zenith. 
And  by  inspection  we  reach  the  general  proposition  that 
parallax  lessens  altitude,  and  its  effect  decreases  as  altitude 
increases,  until  it  becomes  zero  when  the  body  is  exactly 
in  the  zenith.  Both  parallax  and  refraction  vanish  at 
the  zenith;  but  at  all  other  altitudes,  their  effects  are 
just  opposite,  refraction  always  seeming  to  elevate,  and 
parallax  to  depress,  the  heavenly  bodies. 

How  the  Distance  of  the  Moon  is  found.  —  By  precisely 
the  principle  of  the  illustration  on  page  234  is  the  distance 
of  the  moon  from  the  earth  found  —  that  is,  by  calculation 
from  its  parallax.  And  the  parallax  can  be  found  only  by 
observations  from  two  widely  distant  stations  on  the  earth. 


Moon's  Deviation  from  a  Straight  Line    237 


Imagine  a  being  of  proportions  so  huge  that  his  head  would  be  as 
large  as  the  earth.  Then  think  of  his  two  eyes  as  two  observatories ; 
for  example,  Berlin  and  Capetown,  one  in  the  northern  and  one  in  the 
southern  hemisphere.  Also  imagine  the  moon  to  take  the  place  of  the 
screw  and  replace  the  divisions  on  the  rule  by  fixed  stars.  Evidently 
then,  the  observer  at  Berlin  will  see  the  moon  close  alongside  of  differ- 
ent stars  from  those  which  the  Capetown  observer  will  see  adjacent 
to  the  edge.  The  amount  of  displacement  can  be  judged  from  this 
illustration,  which  shows  the  well- 
known  group  of  stars  called  the 
Pleiades  in  the  constellation  Taurus. 
The  bright  disk  represents  the  moon 
as  seen  from  Berlin,  the  darker  disk 
where  seen  from  Capetown.  As  the 
angular  distances  of  all  these  stars 
from  each  other  are  known,  the  an- 
gular displacement  of  the  moon  in 
the  sky  (or  its  parallax  referred  to 
the  line  joining  Berlin  and  Capetown 
as  a  base)  can  be  found.  Now  the 
length  of  this  straight  line,  or  cord, 
through  the  earth's  crust  is  known, 
because  the  size  of  the  earth  is 
known.  So  it  is  evident  that  the 
distance  of  the  moon  can  be  calcu- 
lated from  these  data.  The  process, 
however,  requires  the  application  of 
methods  of  plane  trigonometry.  It 
was  primarily  for  the  purpose  of  find- 
ing the  moon's  distance  that  the  Royal  Observatory  at  Capetown  was 
founded  by  the  British  government  early  in  the  present  century. 

Moon's  Deviation  from  a  Straight  Line  in  One  Second.  — 

As  the  moon's  distance  from  the  earth  is  approximately 
240,000  miles,  the  circumference  of  her  orbit  (considered 
as  a  circle)  is  1,509,000  miles.  But  our  satellite  passes 
over  this  distance  in  27  d.  7  h.  43  m.  11.55.;  therefore  in  one 
second  she  travels  0.604  mile.  In  that  short  interval  how 
far  does  her  path  bend  away  from  a  straight  line,  or  tan- 
gent to  her  orbit  ? 

Suppose  that  in  one  second  of  time  the  moon  would  move  from  S 
to  7"1,  if  the  earth  exerted  no  attraction  upon  her.     On  account  of  this 


Moon  as  seen  from  Berlin  and 
Capetown 


OF  THE 


238 


The  Moon 


attraction,  however,  she  passes  over  the  arc  6V.     This  arc  is  0.604 
in  length,  or  about  ©".5  as  seen  from  the  earth;  and  as  this  angle  is 

very  small,  the  arc  •  St  may  be  re- 
garded as  a  straight  line,  so  that  StU 
is  a  right  angle.  Therefore 

SU  :  St  :  :  St  :  Ss 

But  SfJ  is  double  the  distance  of  the 
moon  from  us ;  therefore  Ss  is  0.053 
inch, "  which  is  equal  to  Tt,  or  the 
distance  the  moon  falls  from  a  straight 
line  in  one  second. 

So  that  we  reach  this  re- 
markable result :  The  curva- 
ture of  the  moon's  path  is  so 
slight  that  in  going  -^  of  a 
mile,  she  deviates  from  a 
straight  line  by  only  -fa  of  an 
inch. 

Dimensions  of  the  Moon.  —  First  her  apparent  diameter  is 
measured :  it  is  somewhat  more  than  a  half  degree  (accu- 
rately, the  semidiameter  is  15'  32". 6).  But  the  moon's 
parallax,  or  what  is  the  same  thing,  the  angle  filled  by  the 
earth's  radius  as  seen  from  the  moon,  is  57'.  So  that, 
as  the  length  of  the  earth's  radius  is  3960  miles,  we  can 
form  the  proportion  — 


Fall  of  Moon  in  One  Second 


Radius  of  earth 
as  seen  from  moon 

57 


Radius  of  moon     )  ..  (  Length  of  earth's  )  .  (  Length  of  moon's 
as  seen  from  earth  I  *"  |    radius  in  miles    \  '  )     radius  in  miles 


15-5 


3960 


10/7 


The  diameter  of  the  moon,  therefore,  from  this  proportion 
is  2154  miles.  A  more  exact  value,  as  found  by  astrono- 
mers from  a  calculation  by  trigonometry  is  2 1 60  miles.  The 
moon's  breadth,  then,  somewhat  exceeds  one  fourth  the 
diameter  of  our  globe.  So  far  as  known,  the  diameter  is 
the  same  in  all  directions ;  that  is,  the  moon  is  spherical. 
As  surfaces  of  spheres  vary  with  the  squares  of  their 


To  Measure  the  Moons  Diameter         239 

diameters,  the  surface-area  of  our  satellite  is  about  -^  that 
of  our  planet,  or  4^  times  that  of  the  United  States.  The 
bulk  of  the  moon  is  only  -^  that  of  the  earth,  because 
volumes  of  globes  vary  as  the  cubes  of  their  diameters. 

To  measure  the  Moon's  Diameter.  —  You  need  not  take  the  diameter 
of  the  moon  on  faith  :  measure  it  for  yourself.     When  our  satellite  is 


Measuring  the  Moon's  Diameter  without  Instruments 

within  a  day  or  two  of  the  full,  select  a  time  from  a  half  hour  to  three 
hours  after  moonrise.  Open  a  window  with  an  easterly  exposure,  close 
one  of  the  shutters,  and  turn  its  slats  (opposite  the  open  sash)  so  that 
their  planes  shall  be  directed  toward  the  moon.  The  observation  now 
consists  of  four  parts:  (i)  so  placing  the  head  that  the  moon  can  be 
seen  through  the  slats,  (2)  making  the  distance  of  the  eye  from  the 
window  such  that  the  moon  will  just  seem  to  fill  the  interval  between 
two  adjacent  slats,  (3)  measuring  the  eye's  distance  from  the  slats,  (4) 
measuring  the  distance  of  the  slats  from  each  other.  A  pile  of  books 
will  be  a  help  in  fixing  the  point  where  the  eye  was  when  making  the 
observation.  Placing  the  head  beyond  the  books,  and  about  seven  feet 
from  the  sash,  move  slowly  away  from  the  window  till  the  moon  just 
fills  the  space  between  two  adjacent  slats.  Or  if  size  of  the  room  will 
allow,  let  the  moon  fill  the  space  between  two  slats  not  adjacent.  Make 
a  mark  on  the  frame  of  the  shutter  between  these  slats.  Bring  the  pile 


240  The  Moon 

of  books  close  up  to  the  eye  so  that  a  near  corner  of  the  top  book  may 
mark  where  the  eye  was.  Next  thing  necessary  is  a  non-elastic  cord 
about  15  feet  long.  Tie  one  end  to  the  slat  or  frame,  near  mark  just 
made,  then  draw  it  taut  to  corner  of  pile  of  books  where  the  eye  was. 
Measure  along  the  cord  the  distance  (in  inches)  of  the  eye  from  the 
slats.  Also  measure  perpendicular  distance  (in  inches)  between  the 
inner  faces  of  the  two  slats  marked.  Then  approximate  diameter  of 
moon  (in  miles)  is  found  from  the  following  proportion  :  — 

f  Distance  of  |     f  distance  of  )  f  diameter  of  1 

j    slats  from    \  :  \    slats  from    (•  :  :  239,000  :  j     the  moon    [ 
(      the  eye      J     I  each  other  J  I     (in  miles)  J 

Repeat  observation  at  least  twice,  moving  pile  of  books  each  time, 
adjusting  it  anew,  and  measuring  distance  over  again. 

Measures  of  the  Moon  and  their  Calculation.  —  On  i8th 
January,  1897,  at  about  6  o'clock  P.M.,  or  an  hour  after 
the  moon  had  risen,  the  following  measures  were  made :  — 

Distances  of  Perpendicular  distance  between 

shutter  from  eye.  inner  faces  of  slats. 

(1)  139.5  inches.  i^  inches. 

(2)  136  239,000 

(3)  ]37_  — 


.3. 

2170 

So  the  moon's  diameter  from  these  crude  measures  is 
2 1 70  miles,  only  about  ^-^  Part  to°  great. 

Why  the  Moon  seems  Larger  near  the  Horizon.  —  Because  of  an 
optical  illusion.  With  two  strips  of  blank  paper,  cover  everything 
near  the  bottom  of  this  page  except  the  line  of  dots.  Before  reading 
further,  decide  which  seems  longer,  xy  or  yz  ? 


Distance  almost  invariably  seems  longer  if  there  are  many  interven- 
ing objects.  For  example,  xy  seems  longer  than  yz,  because  xy  is 
filled  with  dots,  and  yz  is  not.  Thus  horizon  appears  to  be  more 
distant  than  zenith,  because  the  eye,  in  looking  toward  the  horizon, 
rests  upon  many  objects  by  the  way.  This  accounts  for  the  apparent 
flattening  of  the  celestial  vault.  Now  the  moon  near  the  horizon  and 


Moon  really  Largest  at  the  Zenith         241 

at  the  zenith  is  seen  to  be  the  same  object  in  both  positions ;  but  when 
near  the  horizon  she  seems  larger  because  the  distance  is  apparently 
greater,  the  mind  unconsciously  reasoning  that  being  so  much  farther 
away,  she  must  of  course  be  larger  in  order  to  look  the  same.  Often  the 
sun  is  seen  through  thick  haze  or  fog  near  the  horizon,  and  a  like 
illusion  obtains.  But  we  know  that  the  true  dimensions  of  these  bodies 
do  not  vary  in  this  manner,  nor  do  their  distances  change  sufficiently. 
And  whether  illusion  of  sun  or  moon,  it  is  easy  to  dispel.  Roll  a  thin 
sheet  of  paper  round  a  lead  pencil,  making  a  tube  about  12  inches 
long.  With  one  eye  look  through  this  tube  at  the  much-enlarged  sun 
or  moon  near  the  horizon ;  instantly  the  disk  will  shrink  to  normal  pro- 
portions. Then  close  this  eye  and  open  the  other  —  as  instantly  the 


Why  the  Moon  is  really  largest  at  the  Zenith 

illusion  deceives  again.  Repeat  the  experiment,  opening  and  closing 
the  eyes  alternately  as  often  as  desired  ;  the  eye  behind  the  tube  is 
never  deceived,  because  it  sees  only  a  narrow  ring  of  sky  round  the 
moon,  and  the  tube  cuts  off  all  sight  of  the  intervening  landscape. 

Moon  Larger  at  Zenith  than  at  Horizon.—  The  actual  fact  is  just  the 
reverse  of  the  illusion  ;  for  if  the  moon's  horizontal  diameter  is  measured 
accurately  when  near  the  horizon,  it  is  actually  less  than  on  the  meri- 
dian. The  above  diagram  makes  this  at  once  apparent.  The  moon 
at  M  is  in  the  horizon  of  a  place  A  on  the  surface  of  the  earth,  and 
in  the  zenith  of  B,  which  may  be  conceived  the  same  as  A,  after  the 
earth  has  turned  about  90°  on  its  axis.  As  M  is  nearer  B  than  A  by 
almost  the  length  of  the  earth's  radius,  or  nearly  4000  miles,  clearly  the 
zenith  moon  must  be  larger  than  the  horizon  moon  by  about  ^ff  part 
because  CB  is  about  ^  of  CM. 

The  Moon's  Mass. — The  mass  of  the  moon  is  81  times 
less  than  that  of  the  earth ;  partly  because  of  her  smaller 
size,  and  partly  because  materials  composing  our  satellite 
are  on  the  average  only  three  fifths  as  dense  as  those  of 
the  earth. 

TODD'S  ASTRON.  —  1 6 


242  The  Moon 

Gravity  at  the  moon's  surface  is  about  \  that  of  the  earth :  it  is  only 
•fa  as  great  because  of  the  moon's  smaller  mass ;  but  greater  by  14 
times  because,  as  will  be  explained  in  a  later  chapter,  gravity  increases 
as  the  square  of  the  distance  from  the  center  of  attraction  becomes  less  ; 
and  the  square  of  the  moon's  radius  is  about  14  times  less  than  the 
square  of  the  earth's.  Surface  gravity  on  the  moon  is  therefore  \\ ,  or 
about  £,  that  on  the  earth.  So  a  man  weighing  144  pounds  would 
weigh  only  24  pounds  on  the  moon,  if  weighed  by  a  spring  balance. 
An  athlete  who  is  applauded  for  his  standing  jump  of  78  inches  could, 
with  no  greater  expenditure  of  muscular  energy,  jump  39  feet  on  the 
moon.  Probably  this  deficiency  of  attraction  at  the  moon's  surface 
explains,  too,  why  many  of  the  lunar  mountains  are  much  higher  than 
ours.  Our  satellite's  attraction  for  the  oceans  of  the  earth,  produc- 
ing tides,  is  a  basis  of  one  method  of  weighing  the  moon.  Another 
method  is  by  the  moon's  influence  on  the  motion  of  the  earth :  when 
in  advance,  or  at  third  quarter  the  moon's  attraction  quickens  our  motion 
round  the  sun  as  much  as  possible ;  when  behind  the  earth  in  its  orbit, 
or  at  first  quarter,  our  satellite  retards  our  orbital  motion  round  the 
sun  by  the  greatest  possible  amount. 

Axial  Rotation.  —  Our  globe  revolves  on  its  axis  about 
30  times  more  swiftly  than  the  moon  does.  For  while 
our  day  is  23  h.  56  m.  long,  the  lunar  day  is  equal  to  29^ 
of  our  days ;  that  is,  the  moon  turns  round  once  on  her 
axis  while  going  once  round  the  earth. 

The  simplest  sort  of  an  experiment  will  clearly  illustrate  this :  let  a 
lighted  lamp  represent  the  sun ;  the  teacher  standing  in  the  middle  of 
the  room  represent  the  earth ;  and  let  a  pupil,  representing  the  moon, 
walk  slowly  around  the  teacher  in  a  circle,  the  pupil  being  careful  to 
keep  the  face  always  turned  toward  the  teacher.  It  will  readily  be  seen 
that  the  pupil  while  walking  once  around  has  turned  his  face  in  succes- 
sion toward  all  objects  on  the  wall.  In  other  words,  he  will  have  made 
one  slow  revolution  on  his  own  axis  in  exactly  the  same  time  it  took 
him  to  walk  once  completely  round  the  teacher.  So  the  two  motions 
being  accomplished  in  just  the  same  time,  a  given  side  of  the  moon  is 
always  turned  toward  the  earth,  just  as  the  face  of  the  pupil  was  always 
toward  the  teacher.  So,  too,  the  opposite  side  of  our  satellite  is  per- 
petually invisible  to  us. 

Librations.  —  By  a  fortunate  dip  of  the  moon's  axis  to 
the  plane  of  the  orbit,  however,  we  are  sometimes  enabled 


No  Lunar  Atmosphere  243 

to  see  a  little  more  of  the  region,  now  around  one  pole,  and 
now  around  the  other.  The  inclination  is  83°  21',  and  our 
ability  to  see  somewhat  farther  over,  as  it  were,  arises  from 
this  libration  in  latitude.  Again,  the  rate  of  the  moon's 
motion  about  the  earth  varies,  while  her  axial  turning  is 
perfectly  uniform,  so  that  one  can  see  around  the  edge 
farther,  alternately  on  the  western  and  eastern  sides; 
this  is  called  libration  in  longitude.  When  the  moon 
is  near  the  zenith,  there  is  little  or  no  effect  of  libration 
due  to  position  of  observer  on  the  earth.  When,  however, 
the  moon  is  in  the  horizon,  observer  is  nearly  4000  miles 
above  the  plane  passing  through  earth's  center  and  the 
moon.  Consequently  he  can  see  a  little  farther  around 
the  western  limb  at  moonrise  and  around  the  eastern  limb 
at  moonset.  This  effect  is  known  as  diurnal  libration. 
As  a  sum  total  of  the  three  librations,  about  four  sevenths 
of  the  moon's  entire  surface  can  be  seen  in  all. 

No  Lunar  Atmosphere.  —  One  reason  for  our  certainty 
that  the  moon  has  no  atmosphere  is  this :  when  our  sat- 
ellite passes  over  a  star  (or  occults  it,  as  the  technical 
expression  is),  disappearance  at  the  edge  of  the  moon  is 
exceedingly  sudden.  There  is  no  dimming  of  the  star's 
light  before  it  is  extinguished,  as  there  would  be  if  partly 
absorbed  by  lunar  air  and  clouds.  The  spectroscope,  too, 
shows  no  change  in  the  star's  spectrum  when  it  is  close  to 
the  moon's  edge.  Also  during  solar  eclipses,  the  moon's 
outline  seen  against  the  sun  is  always  very  sharply  defined. 
Some  writers  have  thought  it  possible  that  there  may  be 
traces  of  water  and  atmosphere  yet  lingering  at  the  bottom 
of  deep  valleys,  but  no  observations  have  yet  confirmed 
this  hypothesis.  Perhaps  the  moon,  in  some  early  stage 
of  her  history,  had  an  atmosphere,  though  not  a  very  ex- 
tensive one ;  and  it  may  have  been  partly  absorbed  by 
lunar  rocks  during  the  process  of  their  cooling  from  an 


244  The  Moon 

original  condition  of  intense  heat,  common  to  both  earth 
and  moon.  Comstock  is  investigating  anew  the  question 
of  a  lunar  atmosphere. 

Why  No  Air  and  Water  on  the  Moon.  —  Supposing  that  these  ele- 
ments once  surrounded  the  moon  in  remote  past  ages,  their  absence 
from  our  satellite  at  the  present  time  is  easy  to  explain  according  to  the 
kinetic  theory  of  gases,  accepted  by  modern  physicists.  This  theory 
asserts  that  the  particles  of  a  gas  are  continually  darting  about  in  all 
possible  directions.  The  molecules  of  each  gas  have  their  own  appro- 
priate or  normal  speed,  and  this  may  be  increased  as  much  as  seven 
fold  in  consequence  of  their  collisions  with  one  another.  From  the 
known  law  of  attraction  it  is  possible  to  calculate  the  velocity  of  a  mov- 
ing body  which  the  moon  is  capable  of  overcoming ;  if  a  rifle  ball  on 
the  moon  were  fired  with  a  velocity  of  about  7000  feet  per  second,  or 
three  times  the  speed  so  far  attained  by  artificial  means  on  the  earth, 
it  would  leave  our  satellite  forever,  and  pursue  an  independent  path  in 
space.  Physicists  have  ascertained  that  the  molecules  of  all  gases 
composing  the  atmosphere  can  have  velocities  of  their  own  far  exceed- 
ing this  limit ;  and  as  earth  and  moon  are  many  millions  of  years  old, 
it  is  easy  to  see  how  the  moon  may  have  completely  lost  her  atmos- 
phere by  this  slow  process  of  dissipation.  Surface  attraction  of  the 
moon,  only  one  sixth  that  of  the  earth,  has  simply  been  powerless  to 
arrest  this  gradual  loss.  The  possible  speed  of  molecules  of  hydrogen 
is  greatest,  and  even  exceeds  the  velocity  which  the  earth  is  able  to 
overcome ;  so  that  this  theory  explains,  too,  the  absence  of  free  hydro- 
gen in  our  own  atmosphere.  Water  on  the  moon  would  gradually 
become  vaporized  into  atmosphere,  and  complete  disappearance  as  a 
liquid  may  readily  have  taken  place  in  this  manner.  Whether  it  may 
be  present  in  the  form  of  ice,  it  is  not  possible  to  say. 

The  Moon's  Light  and  Heat.  — The  amount  of  moonlight 
increases  from  new  to  full  more  rapidly  than  the  illumined 
area  of  the  moon's  disk;  so  our  satellite  at  the  quarter 
gives  much  less  than  half  her  light  at  the  full.  Mainly, 
this  is  due  to  gradually  shortening  shadows  of  lunar  eleva- 
tions, which  vanish  at  the  full.  As  is  very  apparent  to 
the  eye  at  this  phase,  some  parts  of  the  moon  are  much 
darker  than  others ;  but  on  the  average,  the  lunar  surface 
reflects  about  one  sixth  of  the  sunlight  falling  upon  it. 
The  spectroscope  shows  no  difference  in  kind  between 


The  Moon  and  the   Weather  245 

moonlight  and  sunlight.  The  brightness  of  the  full  moon 
is  deceptively  small,  being  at  average  distance  only  6  0  Q*Q  0  0 
that  of  the  sun.  Heat  from  the  full  moon  is  nearly  four 
times  greater  than  the  amount  of  light,  and  the  larger 
part  of  it  is  heat,  not  reflected,  but  radiated  from  the  moon 
as  if  first  absorbed  from  the  sun.  Our  satellite  having  no 
atmosphere  to  help  retain  this  heat,  it  radiates  into  space 
almost  as  'soon  as  absorbed,  so  that  temperature  at  the 
lunar  surface,  even  under  vertical  sunlight,  probably  never 
rises  to  centigrade  zero.  At  the  end  of  the  fortnight 
during  which  the  sun's  rays  are  withdrawn,  temperature 
must  drop  to  nearly  that  of  interplanetary  space,  proba- 
bly about  300°  below  zero.  In  America  Langley  and 
Very  are  foremost  in  this  research. 

The  Moon  and  the  Weather. — A  wide,  popular  belief,  hardly  more 
than  mere  superstition,  connects  the  varying  position  of  the  lunar 
cusps  with  the  character  of  weather.  The  line  of  cusps  is  continu- 
ally changing  its  angle  with  the  horizon,  according  to  the  relation  of 
ecliptic  (or  moon's  orbit)  to  the  horizon,  as  already  explained ;  and 
it  is  impossible,  therefore,  to  see  how  or  why  this  should  indicate  a 
wet  moon  or  a  dry  moon.  As  for  changes  of  weather  occasioned  by, 
or  occurring  coincidently  with,  the  moon's  changing  phases,  one  need 
only  remember  that  the  weekly  change  of  phase  necessarily  comes  near 
the  same  time  with  a  large  per  cent  of  weather  changes ;  and  these 
coincidences  are  remembered,  while  a  large  number  of  failures  to  coin- 
cide are  overlooked  and  forgotten.  Weather,  too,  is  very  different  at 
different  localities,  and  probably  there  is  always  a  marked  change  going 
on  somewhere  when  our  satellite  is  advancing  from  one  phase  to 
another.  Critical  investigation  fails  to  reveal  a  decided  preponderance 
either  one  way  or  the  other,  and  any  seeming  influence  of  the  moon 
upon  weather  is  a  natural  result  of  pure  chance.  The  full  moon,  too,  is 
popularly  believed  to  clear  away  clouds ;  but  statistical  research  does 
not  disclose  any  systematic  effect  of  this  nature.  Moon's  apogee  and 
perigee  are  known  to  occasion  a  periodic  disturbance  of  magnetic 
needles,  and  may  possibly  be  concerned  in  the  phenomena  of  earth- 
quakes ;  but  the  latter  effect  is  not  yet  fully  established. 

Surface  of  the  Moon.  —  In  days  of  earlier  and  less  perfect 
telescopes,  darker  patches  very  noticeable  on  the  moon's 


246  The  Moon 

disk  were  named  seas,  and  these  titles  still  cling  to  them, 
although  it  is  now  known  that  they  are  only  desert  plains, 
and  not  seas.  All  the  more  important  features  can  be 
accurately  located  from  the  accompanying  illustration. 


Telescopic  Features  of  the  Moon  as  seen  in  an  Inverting  Telescope 

Since  great  modern  telescopes,  using  a  power  of  1 500  bring 
the  moon  within  about  150  miles,  much  detail  can  be  seen 
in  the  inexpressibly  lonely  scenery  diversifying  our  satellite. 
A  great  city  might  be  made  out,  but  the  greatest  building 
ever  built  on  our  earth  could  not  be  seen  except  as  a  mere 
speck.  Also  the  best  modern  photographs,  like  those  re- 


Surface  of  the  Moon 


247 


produced  on  pages  16  and  248,  are  amply  sufficient  for 
critical  study;  and  examination  of  them  is  much  more 
satisfactory  than  the  ordinary  view  through  a  telescope. 
The  '  seas,'  so-called,  may  in  truth  be  the  beds  of  primeval 


.^MASKELYNE  (   TRIESNECKER 

itatis     1*         Mare       °  f\°     O 


NORTH    POLE 
Key  to  the  Chart  of  the  Moon  Opposite 

oceans,  which  have  dried  up  and  disappeared  hundreds  of 
thousands  of  years  ago.  They  are  not  all  at  the  same 
level.  Earlier  stages  of  cosmic  life  are  characterized  by 
intense  heat ;  but  as  development  of  the  moon  progressed, 
original  heat  gradually  radiated  into  space,  leaving  her 
surface  finished.  Evidently  she  has  gone  through  experi- 


248 


The  Moon 


ences  some  of  which  the  earth  may  already  have  known, 
and  through  others  still  in  our  remote  future.     Being  so 

much  smaller 
than  the  earth, 
as  well  as  less  in 
mass,  our  satel- 
lite cooled  much 
faster  than  the 
parent  planet.  A 
few  surface  feat- 
ures are  to  be 
explained  as  due 
to  the  consequent 
shrinkage. 

Maps  and  Pho- 
tographs of  the 
Moon.  —  All  the 
lunar  mountains, 
plains,  and  cra- 
ters are  mapped 
and  named;  and 
astronomers  are 
quite  as  familiar 
with  '  Coperni- 
cus '  and  '  Eratos- 
thenes '  (a  great 
crater,  and  a 
mountain  nearly 
1  6,000  feet  high) 
as  geographers 

Moon's  North  Cusp  (photographed  by  the  Brothers  Henry        are     with      VeSU- 
of  the  Paris  Observatory) 


yus 


an(j 


Matterhorn.     Hevelius  of  Danzig  made  the  first  map  of 
the  moon  in  1647.     He  named  the  mountains  and  craters 


The  Mountains  on  the  Moon  249 

and  plains  after  terrestrial  seas  and  towns  and  mountains. 
But  Riccioli,  who  made  a  second  lunar  map  some  time 
after,  renamed  the  moon's  physical  features,  immortalizing 
in  this  way  himself  and  many  friends.  His  names,  with 
numerous  modern  additions,  are  still  current. 

One  astronomer  has  counted  33,000  craters  on  the  moon,  of  course  on 
only  the  four  sevenths  of  her  surface  ever  turned  toward  us  ;  and  as  there  is 
no  reason  for  supposing  the  remainder  to  contain  features  differing  in  kind 
from  those  on  the  hemisphere  so  familiarly  known,  probably  there  are 
not  less  than  60,000  craters  on  the  entire  surface  of  our  satellite.  Dur- 
ing the  last  half  century  many  astronomers  have  interested  themselves 
in  producing  photographs  of  the  moon,  with  very  remarkable  success. 
By  an  exposure  of  a  second  or  two,  a  vast  degree  of  detail  is  secured 
with  perfect  accuracy,  which  the  pencil  could  not  depict  in  months ;  in- 
deed, critical  study  with  a  microscope  has  brought  to  light  lesser  features 
of  hill  and  valley  which  had  escaped  the  eye  and  the  telescope  alone. 
Photographic  maps  or  atlases  of  the  moon  on  a  very  large  scale  have 
recently  been  published  by  the  Paris  Observatory,  the  Lick  Observatory, 
and  the  Prague  Observatory  ;  and  the  material  already  accumulated  will, 
during  the  next  century,  show  any  considerable  changes,  should  such  be 
taking  place. 

Changes  on  the  Moon.  —  Probably  the  observers  who  a  century  ago 
recorded  volcanoes  in  activity  and  progressive  changes  on  the  moon 
were  deceived  by  the  highly  reflective  character  of  materials  forming 
the  summits  of  certain  mountains.  Some  craters  are  alleged  to  have 
disappeared,  and  in  other  instances  new  craters  to  have  formed ;  but 
evidence  has  in  no  case  amounted  to  absolute  proof  as  yet.  It  is  still 
an  open  question  whether  surface  activity  of  any  kind  characterizes  the 
lunar  disk,  except  perhaps  on  a  very  small  scale,  too  minute  for  detection 
with  present  instrumental  means.  Varying  conditions  of  illumination 
by  the  sun  are  so  marked,  even  from  hour  to  hour,  that  nearly  all 
reputed  changes  are  sufficiently  explained  thereby.  Size  and  power 
of  the  telescope,  and  in  drawings  the  personal  equation  of  the  artist, 
together  with  the  state  of  atmosphere,  all  tend  to  introduce  elements 
making  sketches  far  from  comparable. 

The  Mountains  on  the  Moon.  —  Although  of  all  the  satel- 
lites of  the  solar  system,  the  moon  is  nearest  the  size  and 
mass  of  its  primary,  still  this  neighbor  world  is  no  copy  of 
the  present  earth.  The  difference  between  them  is  accentu- 
ated in  the  character  of  their  mountains — on  the  earth 


25° 


The  Moon 


ridges  and  mountain  chains  for  the  most  part,  with  rela- 
tively few  craters ;  on  the  moon  quite  the  reverse,  craters 
being  far  in  excess.  In  large  part  they  seem  to  be  volcanic 
in  formation,  but  many  of  the  largest  ones  with  low  walls 
are  probably  ruins  of  molten  lakes.  When  the  mountains 
of  the  moon  are  illuminated  by  a  strong  cross-light  —  as 
along  the  terminator  at  sunrise  and  sunset  —  they  are 


Lunar  Volcanoes 


thrown  into  sharp  relief,  as  in  this  picture  of  lunar  vol- 
canoes, set  opposite  a  model  of  Vesuvius  and  neighboring 
volcanoes  photographed  under  like  circumstances  of 
illumination.  Similar  volcanic  origin  is  self-evident. 

Nearly  40  lunar  peaks  are  higher  than  Mont  Blanc,  and  the  greater 
relative  height  of  lunar  than  terrestrial  peaks  is  doubtless  due  to  lesser 
surface  gravity  of  our  satellite.  The  Leibnitz  Mountains,  perhaps  the 
highest  on  the  moon,  are  30,000  to  36,000  feet  in  elevation,  much 
exceeding  the  highest  peaks  on  earth.  As  there  is  no  softening  atmos- 
pheric effect,  shadows  of  all  lunar  objects  are  so  sharply  denned  that 
the  height,  depth,  and  extent  of  nearly  all  natural  features  of  the  moon's 
surface  can  be  accurately  measured. 


The  Lunar  Cliffs  251 

To  find  the  Height  of  a  Lunar  Mountain.  —  Heights  of  many  moun- 
tains on  the  moon  have  been  found  by  this  method :  with  a  suitable 
instrument,  called  the 
micrometer,  attached 
to  the  telescope  for 
measuring  small  arcs, 
measure  AM,  distance 
of  terminator  from 
peak  of  a  mountain 
which  sunlight  from 
6"  just  grazes.  Length 
of  moon's  radius  AB 
is  known,  and  distance 
AM  is  given  by  the 
measures.  So  the  value  Measuring  Height  of  a  Lunar  Mountain 

oiBM,  or  moon's  aver- 
age radius  as  increased  by  the  height  of  mountain,  can  be  found  by 
solving  the  right-angled  triangle  ABM. 

A  Typical  Crater  highly  magnified.  —  Somewhat  north 
and  east  of  the  center  of  the  lunar  disk  is  the  great  crater 
Copernicus.  Rising  from  its  floor  is  a  cluster  of  conical 
mountains  about  2500  feet  high.  The  walls  of  the  crater 
itself  are  about  50  miles  in  diameter,  and  13,000  feet  high. 
As  the  drawing  on  next  page  shows,  the  surroundings  of 
Copernicus  are  rugged  in  the  extreme,  and  near  full  moon  a 
complex  network  of  bright  streaks  may  be  seen  extending 
more  than  a  hundred  miles  on  every  side.  They  do  not 
appear  in  the  illustration  because  it  was  drawn  near  the 
quarter.  The  streaks  do  not  radiate  from  the  great  crater 
itself,  but  from  some  of  the  craterlets  alongside,  by  which 
Copernicus  is  especially  thickly  surrounded.  Probably  the 
streaks  are  due  to  light-colored  gravel  or  powder  scattered 
radially.  Most  of  the  adjacent  craterlets  are  very  minute, 
and  they  are  counted  by  hundreds. 

The  Lunar  Cliffs  or  Rills  and  Other  Features.  —  Almost  at  the  center 
of  the  moon,  but  slightly  toward  the  northwest,  is  Triesnecker,  a  well- 
pronounced  crater,  along  the  west  side  of  which  is  the  remarkable  cliff 


252 


The  Moon 


system  shown  opposite.  Their  radiation  and  intersection  are  strongly 
marked  —  chasms  about  a  mile  in  breadth,  and  nearly  300  miles  in 
length.  Little  is  known  about  their  nature  and  even  less  about  their 
origin.  The  bottom  of  the  cliffs  is  seen  to  be  nearly  flat,  presenting 
to  some  extent  the  appearance  of  an  ancient  river  bed.  The  few  moun- 
tain chains  on  the  moon  resemble  those  on  the  earth  in  one  respect 

they  are  much 
steeper  on  one  side 
than  on  the  other, 
as  if  the  tiltings  had 
been  similarly  pro- 
duced. Craggy  and 
irregular  pyramids 
are  sparsely  scat- 
tered on  the  plains. 
There  are  many 
valleys,  some  wide 
and  deep,  others 
mere  clefts  or 
cracks.  The  term 
rill  is  often  applied 
to  them  although 
waterless,  and  there 
are  many  hundreds, 
passing  for  the  most 
part  through  seas 
and  plains,  though 
occasionally  inter- 
secting the  craters. 
Some  are  straight, 
others  bent  and 
branching.  Possi- 
bly they  are  fissures 
in  a  surface  still 
shrinking.  In  a  few 
instances,  the  geo- 
logical feature 
known  as  a  fault  may  be  observed  —  the  crack  is  not  an  open  one, 
and  the  surface  on  one  side  is  higher  than  on  the  other.  Also  there 
are  walled  plains,  from  40  to  150  miles  in  diameter,  with  interiors 
generally  level,  but  broken  by  slight  elevations  and  circular  pits  or 
depressions.  Nearly  the  entire  visible  surface  is  astonishingly  diver- 
sified by  clean-cut  irregularities  looking  much  as  if  neither  water  nor 
atmosphere  had  ever  been  present  on  the  moon.  Even  a  small 


Region  Surrounding  Copernicus  (highly  magnified) 


If  One  Were  to  Visit  the  Moon  253 


telescope  helps  greatly  in  examining  them,  and  their  position  on  or 
near  the  terminator  is  most  favorable  for  their  study.  Intervals  of  a 
double  lunation,  or  59  d.  \\  h.  bring  the  terminator  through  very  nearly 
the  same  objects,  so  that  the  nature  and  extent  of  illumination  are 
comparable. 

If  One  were  to  visit  the  Moon.  —  Of  course  no  human  being  could 
visit  the  moon  without  taking  air  and  water  along  with  him.  But  what 
we  know  about  the  surface  of  our  satellite  enables  us  to  describe  some 
of  the  natural  phenomena. 
Absence  of  atmosphere 
means  no  diffused  light ; 
nothing  could  be  seen 
unless  the  direct  rays  of 
the  sun  were  shining  upon 
it.  The  instant  one 
stepped  into  the  shadow 
of  a  lunar  crag,  he  would 
become  invisible.  No 
sound  could  be  heard, 
however  loud ;  in  fact, 
sound  would  be  impossi- 
ble. A  landslide,  or  the 
rolling  of  a  rock  down  the 
wall  of  a  lunar  crater,  could 
be  known  only  by  the 
tremor  it  produced  — 
there  would  be  no  noise. 
So  slight  is  gravity  that  a 
good  player  might  bat  a 
baseball  half  a  mile  with- 
out trying  very  hard. 
Looking  up,  the  stars 
would  be  appreciably 
brighter  than  here,  in  a 

perpetually  cloudless  sky.  Even  the  fainter  ones  would  be  visible  in 
the  daytime  quite  as  well  as  at  night.  If  one  were  to  land  anywhere  on 
the  opposite  side  of  the  moon  and  remain  there,  the  earth  could  never  be 
seen  ;  only  by  coming  round  to  the  side  toward  our  planet  would  it  become 
visible.  Even  then  the  earth  would  never  rise  or  set  at  any  given  place, 
but  it  would  constantly  remain  at  about  the  same  altitude  above  the 
lunar  horizon.  Earth  would  go  through  all  phases  that  the  moon 
does  here,  only  they  would  be  supplementary,  full  earth  occurring 
there  when  it  is  new  moon  here.  Our  globe  would  seem  to  be  about 
four  times  as  big  as  the  moon  appears  to  us.  Its  white  polar  caps  of 


Triesnecker  and  Lunar  Rills 


254 


The  Moon 


ice  and   snow,  its   dark   oceans,  and  the  vast  but  hazy  cloud  areas 

would  be  conspicuous, 
seen  through  our  upper 
atmosphere.  Faint  stars, 
the  filmy  solar  corona,  also 
the  zodiacal  light,  would 
probably  be  visible  close 
up  to  the  sun  himself;  but 
although  his  rays  might 
shine  for  a  fortnight  with- 
out intermission  upon  the 
lunar  landscape,  still  the 
rocks  would  probably  be 
too  cold  to  touch  with 
safety. 


From  the  chief  lu- 
minary of  our  nightly 
skies,  we  turn  to  an 
investigation  of  dis- 
coveries made  by 
astronomers  concern- 
ing the  orb  of  day, 
describing  at  the 
same  time  instru- 
ments and  processes 
of  the  'new  astron- 
omy '  with  which  many  of  these  researches  have  been 
conducted. 


Typical  Lunar  Landscape  (full  Earth) 


CHAPTER   XI 

THE   SUN 

MAN  in  the  ancient  world  worshiped  the  sun.  Prim- 
itive peoples  who  inhabited  Egypt,  Asia  Minor, 
and  western  Asia  from  four  to  eight  thousand 
years  ago  have  left  on  monuments  evidence  of  their  vene- 
ration of  the  '  Lord  of  Day.'  Archaeologists  have  ascer- 
tained this  by  their  researches  into  the  world  of  the 
ancient  Phoenicians,  Assyrians,  Hittites,  and  other  nations 
now  passed  from  earth.  A  favorite  representation  of 
the  sun  god  among  them  was  the  'winged  globe,'  or 
'winged  solar  disk,'  types  of  which  are  well  preserved 
on  the  lintels  of  an  ancient  Egyptian  shrine  of  granite  in 
the  temple  at  Edfu.  In  the  Holy  Scriptures  are  repeated 
allusions  to  the  protecting  wings  of  the  Deity,  referring 
to  this  frequently  recurring  sculptured  design ;  and  we 
know  that  if  his  life-giving  rays  were  withheld  from  the 
earth,  every  form  of  human  activity  would  speedily  come 
to  an  end. 

The  Sun  dominates  the  Planetary  System.  —  The  sun 
is  important  and  magnificent  beyond  all  other  objects  in 
the  universe,  not  only  to  us,  inhabitants  of  the  earth, 
but  to  dwellers  on  other  planets,  if  such  there  be.  All 
these  bodies  journey  round  him,  obedient  to  the  power 
of  his  attraction.  Upon  his  radiant  energies,  lavishly 
scattered  throughout  space  as  light  and  heat,  is  dependent, 
either  directly  or  indirectly,  the  existence  of  nearly  every 
form  of  life  activity;  and  the  transformation  of  solar 

255 


256 


The  Sun 


energy  produces  almost  every  variety  of  motion  upon 
the  earth,  whether  animate  or  inanimate.  The  more 
primitive  the  civilization,  the  more  apparent  is  the  depend- 
ence of  man  upon  the  sun. 

Activities  in  Labrador  here  pictured  are  an  excellent  illustration. 
Without  the  sun's  vitalizing  action,  the  trees,  whose  trunks  and 
branches  furnished  the  load  on  the  sled,  not  to  say  the  sled  itself, 


In  Labrador  (Activities  originating  in  the  Sun) 

could  not  have  grown.  The  food,  whether  animal  or  vegetable,  upon 
which  the  life  and  energy  of  man  and  dog  depend,  would  not  have 
been  possible  without  the  sun.  Creatures  of  land  and  sea,  whose 
skins  provided  the  straps  by  which  the  sled  is  drawn,  could  not  long 
live  without  warmth  and  vitality  lavished  by  the  sun.  Nor  must  we 
overlook  the  farther  fact  pertaining  to  natural  movements  and  phenom- 
ena of  the  air :  for  the  sun  provides  even  the  breeze  to  bulge  the  sail, 
and  he  has  raised  from  the  sea  and  diffused  over  the  land  the  mois- 
ture which  descends  as  snow,  for  the  sled  to  slide  upon.  In  the 
complicated  life  of  our  higher  civilization,  the  sun  is  still  all-powerful, 
though  the  links  in  the  chain  of  connection  are  in  places  concealed. 
Our  comforts  and  activities  are  largely  dependent  upon  heat  given  out 
by  burning  coal ;  but  it  was  through  the  action  of  the  sun's  rays  that 


ff 
Unit 


forests  in  an  early  geologic  age  could  wrest  carbon  from  the  atmosphere 
and  store  it  in  this  permanent  mineral  form,  so  useful  —  one  might 
almost  say  necessary  —  in  the  processes  of  modern  life  In  everything 
material  the  sun  is  our  constant  and  bountiful  benefactor. 


Sun's  Distance  the  Unit  of  Celestial  Measurement.  —  The 

distance  between  centers  of  sun  and  earth  is  the  measur- 
ing unit  of  the  universe.  Although  motions  and  relative 
distances  of  heavenly  bodies  may  be  known,  still  their 
true  or  absolute  distances  cannot  be  found  with  accuracy, 
unless  the  fundamental  unit  is  itself  precisely  determined. 
It  is  as  if  one  were  to  try  to  measure  the  size  of  a  house 
with  a  lead  pencil ;  it  would  be  possible  to  find  the  dimen- 
sions of  the  house  in  terms  of  the  lead  pencil,  but  the 
actual  size  of  the  building  would  not  be  known  until  the 
length  of  the  pencil,  or  unit  of  measure,  had  been  ascer- 
tained. The  distance  of  the  sun  is  this  unit.  A  method 
of  finding  the  distance  of  the  moon  has  been  given,  but 
the  sun's  distance  is  too  great  to  be  measured  in  this  way 
—  even  the  whole  diameter  of  the  earth  is  not  long  enough 
to  form  a  suitable  base  for  the  slender  triangle  drawn  from 
its  antipodes  to  the  sun. 

For'the  proper  application  of  this  method  of  finding  distances,  the 
triangle  included  between  distant  object  and  the  two  ends  of  the  base 
line,  must  be  well-conditioned.  Such  a  triangle  is 
shown  in  the  figure,  in  which  the  width  of  an 
impassable  stream  is  found  by  measuring  on  the 
left  bank  a  distance  nearly  equal  to  the  breadth 
of  the  stream  itself.  An  ill-conditioned  triangle 
is  one  whose  base  is  very  short  in  comparison 
with  its  other  two  sides.  Such  a  triangle  is  shown 
on  page  235,  where  the  base  (or  earth's  diameter) 
is  only  ^  of  the  other  sides.  Base  remaining  the 
same,  the  farther  away  the  object,  the  more  ill-con- 
ditioned the  triangle.  As  the  sun  is  nearly  400 
times  farther  than  the  moon,  the  relation  of  base 
to  other  sides  is  only  TT^.  The  triangle  is,  therefore,  so  ill-condi- 
TODD'S  ASTRON. — 17 


258  The  Sun 

tioned  that  this  direct  method  of  finding  the  sun's  distance  becomes 
inapplicable,  and  other  methods  are  always  relied  upon. 

Finding  the  Sun's  Parallax.  —  On  those  rare  occasions 
when  Venus,  a  planet  nearer  the  sun  than  our  earth  is, 
comes  in  her  path  exactly  between  us  and  the  sun,  she 
moves  like  a  small  black  dot  across  the  shining  disk. 
This  happens  but  twice  in  each  century.  Two  observers 
widely  separate  on  our  globe,  will  see  Venus  projected 
upon  different  portions  of  the  sun's  disk  at  the  same  time ; 
as  on  page  234,  pin  is  seen  against  different  parts  of  scale 
when  viewed  through  the  two  peepholes.  So  the  apparent 
path  of  Venus  across  the  sun  will  be  farther  south  on  the 
disk,  as  seen  from  northern  station ;  and  farther  north  as 
seen  from  southern  one.  Difference  of  the  two  paths  leads 
by  suitable  calculation  to  a  knowledge  of  the  angle  which 
radius  of  the  earth  fills,  as  seen  from  the  sun.  This  angle 
is  called  the  sun's  parallax.  Its  value  at  the  average  dis- 
tance of  the  sun  is  called  the  mean  parallax.  The  equa- 
torial radius  of  our  planet  is  taken  as  the  standard,  the 
same  as  in  the  case  of  the  moon ;  also  when  the  sun  is  on 
the  horizon  its  parallax  is  a  maximum,  called  the  horizontal 
parallax.  The  accepted  value  of  the  sun's  mean  equatorial 
horizontal  parallax  is  8". 8.  This  means  that  the  sun  is  so 
remote  that  if  one  could  visit  him  and  look  in  the  direction 
of  the  earth,  our  globe  would  appear  to  be  only  if. 6 
broad,  an  angle  so  small  as  to  be  invisible  to  the  naked 
eye.  A  telescope  magnifying  at  least  four  or  five  diam- 
eters would  be  necessary  to  see  it. 

The  Sun's  Distance.  — The  sun's  parallax  and  the  length 
of  earth's  radius  are  data  for  a  calculation  by  trigonom- 
etry, giving  the  distance  of  the  sun  equal  to  93,000,000 
miles.  Also  this  important  element  may  be  found  by 
aberration.  Knowing  the  velocity  of  light,  it  is  easy  to 
calculate  the  speed  which  the  earth  must  have  in  order  to 


The  Size  of  the  Sun 


259 


produce  the  known  amount  of  aberration  of  the  stars, 
called  the  constant  of  aberration.  So  it  is  found  that  the 
earth's  actual  velocity  is  something  over  i8J  miles  in  a 
second.  From  this  the  length  of  the  circumference  of  the 
orbit  traversed  by  the  earth  in  365^  days  or  one  year  is 
readily  found,  and  from  that  the  diameter  of  the  orbit,  the 
half  of  which  is  the  mean  distance  of  the  sun.  There  are 
many  other  and  more  complicated  methods  of  obtaining 
the  distance  of  the  sun,  and  they  all  agree  within  a  small 
percentage  of  error.  Subtracting  o".oi  from  the  parallax 
is  equivalent  to  increasing  the  sun's  distance  about  105,000 
miles,  and  vice  versa. 


As  Distance  from  Shade  is  to  Size  of  Image,  so  is  Sun's  Distance  to  his  Diameter 

To  measure  the  Size  of  the  Sun.  —  Knowing  the  distance  of  the  sun, 
it  is  very  easy  to  observe  and  calculate  his  real  dimensions.  The  method 
is  similar  to  that  by  which  the  size  of  the  moon  was  measured ;  and  dif- 
ferent only  because  of  the  superior  intensity  of  the  sun's  light.  Instead 


260  The  Sun 

of  looking  directly  at  the  sun,  simply  look  at  the  image  produced  by  the 
sun's  rays  through  a  tiny  aperture.  Every  one  has  noticed  sunlight 
filtering  into  a  darkened  room  through  chinks  between  the  slats  and 
frame  of  a  blind  or  shutter.  Oftentimes  a  series  of  oval  disks  may 
be  seen  on  the  floor.  Their  breadth  depends  upon  (a)  the  diameter 
of  the  sun,  and  (£)  their  distance  from  the  shutter.  Each  oval  disk 
is  a  distorted  solar  image.  If  a  sheet  of  paper  is  held  at  right  angles 
to  the  direction  of  the  sun,  the  oval  disk  becomes  circular,  and  its 
diameter  can  be  measured.  But  as  the  paper  is  carried  toward  the 
shutter,  notice  that  the  disk  grows  smaller  and  smaller.  So  you  must 
measure  its  distance  from  the  shutter  also.  Select  a  time  when  the 
sun  is  not  exactly  facing  a  window,  but  is  a  little  to  the  right  or  left  of 
it,  though  not  more  than  an  hour  in  either  direction.  On  closing  the 
shutters,  and  turning  the  slats,  the  chain  of  disks  on  the  floor  will  usu- 
ally become  visible.  Examine  them  carefully  when  projected  on  a  small 
white  card,  and  select  the  one  which  has  the  sharpest  outline.  Or,  the 
blinds  may  be  thrown  open,  and  sunlight  admitted  through  a  pin-hole 
in  the  shade,  as  in  last  illustration.  Attach  a  sheet  of  white  paper  to 
the  cover  of  a  book ;  so  support  it  that  the  surface  of  the  paper  shall 
be  at  right  angles  to  the  line  from  book  to  sun.  With  a  sharply-pointed 
pencil,  mark  two  short  parallel  lines  on  the  paper,  a  little  farther  apart 
than  the  diameter  of  the  bright  disk.  Move  the  paper  back  until  the 
sun's  image  just  fills  the  space  between  the  two  lines.  Measure  dis- 
tance between  lines ;  also  with  a  non-elastic  cord,  measure  distance 
from  shade  to  paper  on  the  book.  This  completes  the  observation. 

Calculating  the  Observation.  —  As  in  calculating  the  size  of  the  moon 
when  its  distance  is  known,  so  in  computing  the  dimensions  of  the 
sun,  only  the  'rule  of  three'  is  necessary.  On  22d  May,  1897,  size  of 
a  pin-hole  image  of  sun  was  measured  and  found  to  be  1.175  in-  *n 
diameter.  Distance  between  the  card  on  which  the  image  fell  and 
the  aperture  in  shade  was  10  ft.  5.4  in.  So  the  proportion  is  — 

125.4  :  1.175  ::  93,000,000  :  x. 

The  value  of  x  comes  out  871,000  miles,  or  about  T|ff  part  too  great. 
But  this  amount  of  error  is  to  be  expected,  because  the  method  is  a 
crude  one.  Notice,  however,  its  exactness  in  principle.  To  convey 
an  adequate  idea  of  the  sun's  tremendous  proportions  is  practically 
impossible. 

How  Astronomers  measure  the  Sun. — The  principle  of 
their  method  is  exactly  the  same  as  that  just  illustrated ; 
and  their  results  are  more  accurate  only  because  their 
instruments  are  more  delicate,  and  training  in  the  use 


The  Sun  is  a  Sphere  261 

of   them  thorough  and  complete.      The  latest   and   best 
value  of  the  sun's  diameter  is  865,350  miles. 

The  best  method  utilizes  an  instrument  called  the  heliometer,  or  sun 
measurer.  It  is  a  telescope  of  medium  size,  mounted  equatorially  ;  but 
the  essential  point  of  difference  is  in  the  object  glass,  AB,  which  is 
divided  exactly  in  the  middle.  Accurate  mechanical  devices  are  pro- 
vided by  which  B  can  be  slipped 
sidewise  relatively  to  A,  as  in  A) 
the  lower  figure,  and  the  precise 
amount  of  the  motion  recorded. 
Before  the  halves  of  the  glass 
are  moved  apart,  the  sun's  image 
is  a  single,  very  bright  disk,  like 

the     left     hand     of     the     three      Divided  Object     Images  of  Sun  in  Heliometer 
here    shown.     Turn   the    screw  * ] 

separating  the  halves  of  the 
glass,  and  overlapping  images  appear,  as  in  the  middle  figure ;  and  by 
turning  it  far  enough,  the  two  images  of  the  sun  may  be  brought  into 
exact  exterior  contact,  as  in  the  right  hand  of  the  three  images. 
Final  calculation  of  the  sun's  diameter  is  a  tedious  and  complicated 
process,  because  a  great  variety  of  conditions  and  corrections  must  be 
taken  into  account ;  but  the  heliometer  is  the  most  accurate  measur- 
ing instrument  employed  by  modern  astronomers.  The  limit  of 
accuracy  of  measurement  with  the  heliometer  is  an  angle  no  larger 
than  that  which  a  baseball  would  fill  at  New  York  as  seen  from 
Chicago. 

The  Sun  is  a  Sphere.  —  As  the  sun  turns  round  on  his 
axis,  equatorial  diameters  are  measured  in  every  direction. 
As  they  do  not  differ  appreciably  from  the  polar  diameter, 
the  figure  of  the  sun  is  a  sphere.  His  real  diameter  is  not 
subject  to  change ;  but  as  already  shown,  the  sun's  ap- 
parent diameter  varies  from  day  to  day,  in  exact  proportion 
to  our  change  of  distance  from  him.  The  mean  value  is 
almost  32'  o"  (according  to  Auwers,  31'  59". 26). 

The  actual  diameter  of  the  sun  is  difficult  to  determine,  for  a  variety 
of  reasons.  The  heat  of  his  rays  disturbs  the  atmosphere  through 
which  they  travel,  so  that  his  outline,  or  limb,  is  rarely  seen  free  from  a 
quivering  or  wave-like  motion.  Another  reason  is  irradiation,  a  physio- 
logical effect  by  which  bright  objects  always  seem  larger  than  they  really 


262  The  Sun 

are.  Irradiation  increases  as  brightness  of  the  object  exceeds  that  of 
the  background  against  which  it  is  seen.  Error  in  our  knowledge  of  the 
sun's  diameter  is  probably  about  T<yV<r  part  of  the  whole,  or  about  2". 
At  the  distance  93,000,000  miles,  i"  of  arc  is  equivalent  to  450  miles, 
so  that  the  amount  of  uncertainty  in  the  diameter  of  the  sun  is  about 
900  miles. 

The  Sun's  Volume,  Mass,  and  Density. — As  the  sun's 
diameter  is  nearly  no  times  greater  than  that  of  the 
earth,  his  volume  is  almost  1,300,000  times  greater,  be- 
cause volumes  of  spheres  vary  as  cubes  of  their  diameters. 
A  method  of  measuring  the  mass  of  the  sun  is  given  on 
page  386.  To  put  it  simply,  the  sun's  mass  is  found  by 
measuring  the  force  of  his  attraction.  If  sun  and  earth 
are  at  the  same  distance  from  a  given  body,  the  sun  will 
attract  it  330,000  times  more  powerfully  than  the  earth 
does.  Sun's  weight,  in  other  words,  is  330,000  times  as 
great  as  earth's.  A  body  falling  freely  under  the  influ- 
ence of  the  sun's  attraction  would  on  reaching  him  have  a 
velocity  of  383  miles  a  second.  As  the  sun  is  1,300,000 
times  greater  in  volume  than  the  earth,  evidently  he  must 
be  much  less  dense  than  our  globe ;  and  his  component 
materials,  bulk  for  bulk,  must  be  about  one  fourth  lighter 
than  those  of  the  earth.  As  compared  with  water,  the  sun 
is  rather  less  than  i^  times  as  dense. 

Gravity  at  the  Sun's  Surface. — The  weight  of  the 
earth,  it  will  be  remembered,  is  6  x  io21  tons.  But  the 
sun  weighs  330,000  times  as  much,  —  a  numerical  result 
which  the  human  mind  is  utterly  powerless  to  grasp. 
Another  comparison  will  help  to  fix  relative  proportions 
in  memory.  Many  planets  are  vastly  larger  and  more  mas- 
sive than  the  earth.  But  if  all  the  planets  of  the  solar 
system  and  their  accompanying  retinues  of  satellites  were 
fused  together  into  a  single  ball,  it  would  weigh  but  T|^  as 
much  as  the  sun.  So  vast  are  the  dimensions  of  our  cen- 
tral luminary  that  the  force  of  gravity  at  the  surface  is  not 


How  to  Observe  the  Sun 


263 


so  great  as  his  prodigious  mass  would  seem  to  indicate: 
it  is  only  2J\  times  as  great  as  gravity  at  the  surface 
of  the  earth.  A 
body  would  fall  ver- 
tically 444  feet  in 
the  first  second. 
Recall  the  agile 
athlete  who,  when 
transferred  to  the 
moon,  executed  a 
standing  jump  of 
39  feet:  if  at  the 
sun,  he  would  find 
his  movements 
hampered  by  a 
bodily  weight  of 
about  two  tons,  and 
his  '  standing  jump,' 
if  possible  at  all, 
could  not  exceed 

three  inches.  On  the  sun,  the  pendulum  of  an  ordinary 
mantel  clock  would  quiver  or  oscillate  so  rapidly  that  its 
vibrations  could  not  easily  be  counted.  For  every  tick  of 
the  escapement  here,  there  would  be  five  at  the  sun. 

How  to  observe  the  Sun.  —  Unless  the  telescope  is  provided  with  a 
special  eyepiece,  called  a  helioscope,  it  is  dangerous  to  look  at  the  sun 
directly,  because  heat  rays  coming  through  the  dense  colored  glass  cover- 
ing the  eyepiece  are  very  harmful  to  the  delicate  rods  of  the  retina. 
Besides  this,  the  colored  glass  is  liable  to  be  broken  suddenly  by  the 
intense  heat.  If  such  accident  happens  while  the  eye  is  at  the  tele- 
scope, a  dark  spot  in  the  retina  is  pretty  sure  to  result ;  and  it  will  re- 
main permanently  insensitive — an  extreme  case  of  'over-exposure.' 
Rather  look  at  the  sun's  surface  indirectly,  by  projection,  as  in  the  pic- 
ture. To  the  telescope  tube  attach  a  cardboard  screen,  two  or  three  feet 
square,  and  fill  the  chinks  around  the  tube  with  cloth  or  paper.  This 
large  screen  tightly  fastened  to  the  tube,  is  very  necessary  to  keep 


Viewing  the  Surface  of  the  Sun 


264 


The  Sun 


direct  light  of  the  sun  from  falling  upon  the  sheet  of  paper  below,  on 
which  the  sun's  image  is  projected.  This  sheet  may  be  held  in  the 
hand ;  but  it  is  better  to  attach  it  to  a  light  frame,  which  slides  along  a 
stick  firmly  screwed  to  the  side  of  the  telescope  tube.  Then  the  paper 

may  be  kept  always  at 
right  angles  to  the  axis 
of  the  telescope ;  and 
spots  may  be  made  to 
•p-t.jfi^y  l^ok  larger  or  smaller  by 
merely  sliding  the  frame 
toward  or  from  the  eye- 
piece. Careful  focusing 
5^5  is  important,  and  probably 
%&£  it  will  be  necessary  to  re- 
focus  every  time  the  dis- 
tance between  paper  and 
eyepiece  is  changed. 
Ten  or  twelve  persons 
can  readily  observe  sun 
spots  in  this  way  at  the 
same  time,  and  without 
the  slightest  danger  or 
inconvenience.  Surface 
mottlings  and  faculae,  or 
white  spots,  are  finely 
seen.  If  the  telescope  is 
a  large  one,  the  eyepiece 
should  occasionally  be 
taken  out  and  cooled ; 
but  even  a  spyglass  will 
gather  enough  light  to 
show  the  spots  and  other 
details  of  the  sun's  surface. 

The  Photosphere.  —  The  photosphere  is  that  mottled  exterior  of  the  sun 
which  radiates  its  light.  The  photographic  picture  above  shows  its  general 
texture.  The  blurring  is  a  real  phenomenon.  This  rice-grain  structure  can 
nearly  always  be  seen  even  with  moderate  telescopic  power,  because  the 
grains  are  about  500  miles  across.  Under  the  best  conditions  of  vision, 
and  great  increase  of  power,  the  grains  subdivide  into  granules.  Float- 
ing above  the  photosphere,  and  quite  numerous  around  the  sun's  limb, 
may  usually  be  seen  a  number  of  irregularly  connected  whitish  spots,  or 
patches,  called  faculae.  It  is  certain  that  some  of  the  faculas  are  eleva- 
tions, because  they  have  been  seen  projecting  beyond  the  edge  of  the 
disk.  As  will  be  shown  farther  on,  the  faculas  extend  in  zones  all  the 


Photosphere  (photographed  by  Jansseni 


Veiled  Spots 


265 


way  across  the  sun ;  but  they  are  more  obvious  at  the  limb,  because 
general  illumination  of  the  photosphere  in  that  region  is  less,  owing  to 
greater  thickness  of  solar  atmosphere  through  which  rays  from  the 
photosphere  must  pass. 

Sun  Spots.  —  Immense  dark  spots  are  frequently  seen  on 
the  photosphere.  Generally  they  have  a  dark  center, 
called  the  umbra,  and  a  somewhat  lighter  fringe,  called  the 
penumbra,  which  is 
darker  near  its  outer 
edge,  lighter  toward 
the  umbra,  and  often 
shows  a  thatch-work 
structure,  as  in  Sec- 
chi's  drawing  (also 
page  1 1 ).  Of  widely 
varying  shapes  and 
sizes,  they  are  usually 
nearly  circular  at  the 
middle  stage  of  exist- 
ence, though  more 
irregular  at  beginning 
and  end. 


Sun  Spot  highly  magnified  (Secchij 


The  dark  umbra  is  not  all  equally  dark ;  at  times  faint  patches  or 
grains  of  luminous  matter  appear  to  float  above  the  darker  region  under- 
neath. Also  sometimes  appear  tiny  round  spots,  darker  than  the  um- 
bra, known  as  nuclei  —  perhaps  openings  into  still  greater  depths  ;  for 
the  spots  themselves  nearly  always  appear  like  depressions  in  the  pho- 
tosphere, and  on  several  occasions  have  been  seen  as  actual  notches 
at  the  edge  of  the  sun,  as  in  the  next  illustration.  There  is  good 
evidence,  however,  that  many  of  them  are  not  depressions.  If  a  spot 
is  as  large  as  27,000  miles  in  diameter,  it  can  be  seen  without  a  tele- 
scope as  a  very  minute  black  speck.  Occasionally  spots  are  even  larger 
than  this,  and  50,000  miles  is  a  size  not  unknown.  The  largest  sun  spot 
on  record  was  observed  in  1858 ;  it  was  nearly  150,000  miles  in  breadth 
and  covered  about  ^  of  the  whole  surface  of  the  sun. 

Veiled  Spots. — Veiled  spot  is  the  name  given  to  hazy,  darkish 
patches  appearing  now  and  then  upon  all  parts  of  the  solar  disk,  even 


266 


The  Sun 


close  to  the  poles.  They  have  been  seen  to  change  their  ill-defined 
outlines  very  rapidly.  Not  extensively  observed  as  yet,  they  are  never- 
theless regarded  as  kin  to  ordinary  spots,  only  that  the  forces  producing 
them  are  not  intense  enough  to  disrupt  the  photosphere.  Faculae  are 
often  seen  above  them. 


Many  Spots  are  seen  as  Depressions  at  the  Sun's  Limb 

Formation  and  End  of  Spots.  —  Each  spot  or  group  of 
spots  has  its  independent  method  of  formation.  Perhaps 
very  gradual,  through  many  weeks,  spots  have  yet  been 
known  to  attain  full  proportions  in  a  few  hours.  When 
completed,  they  are  roughly  circular ;  but  as  their  end 
draws  near,  the  surrounding  matter  seems  to  approach  and 
crowd  upon  the  umbra,  as  if  to  tumble  pell-mell  into  its 
cavernous  depths.  Very  likely  this  is  what  actually  hap- 
pens. Often  tongue-like  encroachments  of  the  penumbra 
force  themselves  across  the  umbra  (illustrated  in  process 
on  page  u);  and  this  usually  indicates  the  beginning  of  a 
rapid  decline  and  disappearance.  The  chasm  seems  to  be 
rilled ;  and  only  a  slightly  disturbed  surface  (surrounded  by 
faculae  or  white  spots,  which  soon  disperse)  remains  for  a 
brief  time  to  indicate  very  indefinitely  the  place  where 
the  spot  existed.  Sun  spots  are  easiest  of  all  solar  phe- 
nomena to  observe.  Sometimes  exceptional  disturbance 
sets  up  a  motion  so  rapid  and  violent  that  vast  changes 
have  been  seen  within  a  few  minutes'  time,  even  while 
the  observer  was  watching. 

Duration  and  Distribution  of  Spots.  —  Often  spots  are 
carried  across  the  face  of  the  sun  in  its  rotation,  and  they 
become  elliptical  by  foreshortening  as  they  approach  the 


Duration  and  Distribution  of  Spots        267 


edge  and  disappear.  The  following  illustration  shows  how 
this  takes  place.  If  a  spot  lasts  a  fortnight  or  more,  it  will 
again  come  into  view  when  the  sun's  rotation  shall  have 
carried  it  halfway  round.  On  reappearing  at  the  eastern 
limb,  a  spot  is  elliptical  and  very,  narrow  at  first,  and  grad- 


Vi     t 


The  Same  Spot  near  Sun's  Center  and  Edge 

ually  it  seems  to  broaden  into  its  actual  shape  on  facing 
the  earth  more  and  more  squarely.  The  spots  are,  on  an 
average,  two  or  three  months  in  duration,  though  very 
often  lasting  only  a  week,  or  perhaps  even  a  few  days  or 
hours.  The  longest  on  record  lasted  18  months,  in  the 
years  1840  and  1841.  Spots  do  not  appear  on  every  part 
of  the  sun's  disk,  but  they  are  nearly  always  confined  to 
zones  on  both  sides  of  the  solar  equator,  extending  from 
latitude  5°  to  30°.  The  spots  are  most  numerous  in  solar 
latitude  15°,  both  north  and  south,  and. a  few  more  are  seen 
in  the  northern  than  the  southern  hemisphere. 


S.'R 


6TH  DECEMBER  5™  MARCH  6THJUNE 

Apparent  Motion  of  Spots  across  the  Sun 


5TH SEPTEMBER 


The  sun's  equator  is  tilted  about  7°  to  the  ecliptic,  so  that  the  spot 
zones  appear  sometimes  straight  and  sometimes  curved  on  the  sun's 
disk,  as  the  four  figures  show,  for  different  seasons  of  the  year. 


268 


The  Sun 


Early  in  March  the  sun's  south  pole,  and  early  in  September  his  north 
pole,  is  turned  farthest  toward  us.  The  axis  of  the  sun,  if  prolonged 
northward,  would  cut  the  celestial  sphere  near  Delta  Draconis.  In 
April  the  sun's  axis  is  inclined  about  25°  west  of  the  hour  circle  passing 
through  his  center ;  in  October,  about  the  same  amount  to  the  east  of  it. 

Periodicity  of  the  Sun  Spots.  —  Spots  are  not  always 
equally  numerous  on  the  surface  of  the  sun.  At  times 
they  may  be  counted  by  hundreds,  and  again  days,  and 
even  weeks,  will  elapse  without  a  single  spot  being  visible. 
A  well-established  period  is  now  recognized.  Spots  dimin- 
ish in  number  slowly,  all  the  while  appearing  at  lower  and 
lower  latitudes  on  the  sun,  and  they  pass  through  a  mini- 
mum at  about  latitude  5°  both  north  and  south.  Then 
rather  suddenly  there  is  an  outbreak  of  spots,  in  latitude 

about  30°  on  both 
sides  of  the  sun's 
equator,  followed  by 
a  growth  in  number 
and  size  of  the  spots 
to  a  maximum,  after 
which  again  comes 
the  decline  in  number, 


/. 

-^ 

/ 

7 

X 

\ 

//, 

^ 

^ 

^Sj 

* 

^>, 

^-^ 

$ 

'•—  -. 

i  i  § 


Curve  of  Sun  Spots  and  Magnetic  Declination 

size,  and  latitude.  As  a  new  outbreak  in  high  latitudes 
usually  begins  about  two  years  before  final  disappearance 
of  the  zones  of  low  latitude,  it  follows  that  near  minimum 
the  spots,  although  few  in  number,  are  distributed  in  four 
narrow  belts,  two  of  low  and  two  of  high  latitude.  The 
complete  round,  or  spot  period,  is  eleven  years  and  one 
month  in  duration.  From  minimum  to  maximum  is  usually 
about  five  years,  and  from  maximum  to  minimum  about  six 
years.  The  fluctuation  in  latitude  is  called  Spoerer's  *  law 
of  zones.'  Regarding  as  determinant  of  the  true  period, 
not  merely  the  total  number  of  spots,  but  the  number 
as  affected  by  the  law  of  zones,  the  true  sun-spot  cycle 


Facula 


269 


appears  to  be  about  fourteen  years  long,  because  a  new 
zone  breaks  out  in  high  latitudes  while  the  old  one  still 
exists  near  the  equator.  Neither  the  cause  underlying  the 
law  of  zones,  nor  the  reason  for  the  spot  period  itself,  is 
known.  Probably  the  latter  is  due  to  the  outbreak  of 
exceptional  eruptive  forces  held  in  check  during  the  sea- 
sons of  fewest  spots.  The  last  maximum  occurred  in 
1893,  and  the  next  minimum  falls  in  1899  or  1900. 

Do  the  Spots  affect  the  Earth?  —  When  sun  spots  are  most  numerous, 
displays  of  the  aurora  borealis  are  most  frequent  and  brilliant,  and  the 
effects  of  magnetic  storms  are  most  strongly  exhibited  by  fluctuations 
of  magnetic  needles  delicately  mounted  in  observatories,  with  pains- 
taking arrangements  for  recording  all  their  oscillations.  These  effects, 
although  recognized,  are  unexplained.  Wolfer's  diagram  opposite  shows 
how  closely  spot  activity  kept  time  with  fluctuations  of  magnetic 
declination  during  the  years  1886-96.  Even  in  periods  of  largest  and 
most  numerous  spots,  the  amount  of  heat  received  from  the  sun  is  not 
a  thousandth  part  lessened,  and  any  effect  of  periodicity  of  the  spots 
upon  the  weather  is  too  slight  to  be  detected. 

Faculae.  —  On  the  bright  surface  of  the  sun  may  nearly 
always  be  seen  still  brighter  specks  or  streaks,  many 
thousand  miles  in  length, 
and  much  larger  than 
any  of  our  continents. 
Such  faculae  were  dis- 
covered by  Hevelius,  at 
Danzig,  about  the  mid- 
dle of  the  i /th  century. 
They  are  supposed  to 
be  elevated  regions  of 
the  surface,  crests  of 
luminous  matter  protrud- 
ing through  the  general 
and  denser  level  of  the 
photosphere.  The  fac- 
ulae are  very  numerous  around  the  spots.  The  sun's  atmos- 


Zones  of  Invisible  Faculae,  7th  August,  1893 
(photographed  by  Hale) 


270  The  Sun 

phere  absorbs  a  large  percentage  of  its  own  light,  so  that 
the  illumination  of  the  disk  diminishes  gradually  toward 
the  edge  all  around.  On  this  account  the  faculae  are  better 
seen  near  the  edge ;  but  they  exist  in  belts  all  the  way 
across  the  sun's  disk,  and  can  be  so  photographed  at  any 
time  by  the  spectroheliograph  (described  in  a  later  sec- 
tion), although  they  are  invisible  to  ordinary  vision.  These 
invisible  faculae  are  most  abundant  in  the  sun-spot  zones. 
There  is  evidence  that  some  faculae  are  clouds  of  incandes- 
cent calcium,  an  element  strongly  marked  in  the  sun.  The 
invisible  faculae  appear  to  be  related  to  the  prominences 
projected  against  the  photosphere. 

The  Sun's  Rotation  on  his  Axis.  —  The  spots  which  last 
longest  help  most  in  ascertaining  the  time  required  by 
the  sun  in  turning  round  once  on  his  axis.  A  large  num- 
ber of  observations  have  shown  that  a  long-lived  spot  near 
the  sun's  equator,  starting  from  the  center,  will  pass  from 
east  to  west  all  the  way  round  and  return  to  the  center  in 
27^  days.  But  as  the  earth  will  meanwhile  have  moved 
eastward  also,  the  sun's  period  of  rotation,  as  referred  to 
the  stars,  is  25^  days.  This  is  the  length  of  the  true,  or 
sidereal  period.  The  exterior  of  the  sun  is  not  rigid,  as 
the  earth  appears  to  be ;  and  it  is  found  that  spots  remote 
from  the  equator  give  a  longer  period  of  rotation  the 
higher  their  latitude.  At  latitude  45 °,  the  period  of  the 
sun's  rotation  is  about  two  days  longer  than  on  the  equator. 
At  latitude  75°,  the  rotation  period,  as  found  by  Duner  with 
the  spectroscope,  is  38^-  days.  Also  Young,  Crew,  and 
others  have  verified  the  rotation  in  this  manner  in  the 
equatorial  regions.  The  cause  of  acceleration  at  the 
equator  has  not  yet  been  discovered. 

The  faculae  appear  to  have  a  different  law  of  rotation  from  that 
governing  the  spots ;  for  no  matter  what  their  latitude,  they  go  round 
in  less  time  than  spots.  From  careful  measures  of  numerous  lines  in 


Continuous  Spectrum  271 

the  solar  spectrum,  Jewell  has  found  that  acceleration  of  the  sun's 
equator  is  greatest  for  the  higher  or  outer  parts  of  the  solar  atmosphere, 
and  that  the  difference  between  the  rotation  periods  of  the  sun's  outer 
and  inner  atmosphere  amounts  to  several  days. 

The  Spectroscope.  —  Place  a  prism  in  the  path  of  a  slender  beam  of 
sunlight.  It  will  be  refracted  out  of  a  straight  course,  and  will  emerge 
as  a  colored  band.  The  light  is  all  refracted,  but  it  is  not  refracted 
equally  ;  the  red  is  bent  least,  and  the  violet  most.  The  many-colored 
image  produced  in  this  manner  is  called  a  spectrum.  This  unequal 
refraction,  and  decomposition  of  white  light  into  its  primary  colors  is 
called  dispersion.  Upon  it  depend  the  principles  of  spectrum  analy- 
sis, which  is  a  study  of  the  nature  and  composition  of  luminous  bodies 
by  means  of  the  light  which  they  emit.  Usually  the  spectroscope  con- 
sists of  four  parts:  (i)  a  very  narrow  slit  6"  through  which  the  beam 


A  Single-prism  Spectroscope  in  Outline 

of  light  is  admitted,  (2)  a  collimator,  A,  or  small  telescope  at  whose 
focus  the  slit  is  placed,  (3)  a  prism,  P,  or  a  closely  ruled  surface,  which 
effects  the  dispersion  necessary  to  produce  a  spectrum,  (4)  a  view 
telescope,  BE,  for  studying  optically  the  different  regions  of  the  spec- 
trum. In  researches  of  the  present  day,  in  which  photography  plays 
an  important  part,  the  spectroscope  is  usually  constructed  so  that  the 
eyepiece  can  be  removed,  and  a  plate-holder  substituted  in  its  place. 
Spectra  can  then  be  photographed,  and  afterward  examined  at  leisure. 
The  illustration  on  the  next  page  shows  a  modern  spectroscope  as 
adapted  for  photographic  work.  Rays  enter  the  upper  tube  on  the  left. 
Continuous  Spectrum  and  Fraunhofer  Lines.  —  Place  a  candle  before 
the  slit,  and  a  continuous  spectrum  is  produced.  A  continuous  spec- 
trum is  one  which  is  crossed  by  neither  bright  nor  dark  lines ;  the 
colors  from  red  to  violet  blend  insensibly  from  one  to  the  other  in 
succession.  Replace  the  candle  by  a  beam  of  sunlight,  and  observe 


272 


The  Sun 


the  difference :  at  first  sight  the  spectrum  appears  to  be  continuous, 
but  closer  observation  immediately  shows  that  the  band  of  color  is 
crossed  at  right  angles  by  a  multitude  of  fine  dark  lines,  of  different 
widths  and  intensities,  and  seemingly  without  order  of  arrangement. 

This  spectrum  is  a  discontinuous  spectrum.     The  dark 
lines  are  called  Fraunhofer  lines,  from  Fraunhofer,  who 


Brashear's  Universal  Spectroscope  (arranged  for  Photographic  Research) 

first  made  a  chart  of  their  position  in  the  prismatic  spec- 
trum. He  designated  the  more  strongly  marked  lines  by 
the  first  letters  of  the  alphabet,  the  A  line  being  in  the 
red,  and  the  H  line  in  the  violet.  Their  character  and 
position  in  the  spectrum  are  highly  significant ;  for  they 
indicate  the  chemical  elements  of  which  luminous  bodies, 
especially  the  sun,  are  composed. 


Normal  Solar  Spectrum 


273 


Normal  Solar  Spectrum.  —  If  the  spectrum  is  formed  by 
passing  the  rays  through  a  prism,  as  in  the  illustration, 
(page  271),  relative  position  of  the  dark  lines  will  vary  with 
the  substance  composing  the  prism  P ;  the  amount  of  dis- 
persion in  different  parts  of  the  spectrum  varies  with  the 
material  of  the  prism.  Another  method  of  producing  the 
spectrum  is  therefore  employed :  by  reflecting  the  sun's 
rays  from  a  grating,  A,  accurately  ruled  with  a  diamond 


A  Diffraction  Spectroscope  in  Outline 

point  upon  polished  speculum  metal,  thousands  of  lines  to 
the  inch,  a  diffraction  spectrum  is  formed.  In  this  case 
dispersion  is  entirely  independent  of  the  material  of  the 
grating ;  and  the  spectrum  is  called  the  normal  solar  spec- 
trum, because  the  amount  of  dispersion  of  the  rays  is 
proportional  to  their  wave  length. 


, 

;  ' 

3 

i              D                ( 

0 

i       / 

NORMAL 
SPECTRUM 

1      I 

1 

PRISMATIC 

1 

1                  ( 

1                   1 

>E           D        f 

hU 

II   1 

| 

SPECTRUM 

VIOLET  GREEN  RED 

Normal  and  Prismatic  Spectra  of  Equal  Length  (Middle  of  both  Spectra  at  D) 

The  diagram  gives  a  comparison  of  the  two  types  of  spectrum.     The 
middle  of  the  spectrum  is  practically  coincident  with  the  yellow  D  lines 
of  sodium.     As  referred  to  the  normal  spectrum,  the  red  end  of  a  pris- 
TODD'S  ASTRON.  — 1 8 

r 


274  The  Sun 

matic  spectrum  is  very  much  compressed ;  and  its  violet  end  similarly 
expanded.  The  finest  gratings  are  ruled  with  a  dividing  engine  perfected 
by  Rowland.  The  precision  of  its  working  is  such  that  the  number  of 
parallel  lines  which  can  be  ruled  on  a  plate  of  metal  an  inch  square 
exceeds  20,000 ;  but  one  tenth  this  number  is  a  good  working  limit. 

High  Power  Spectroscopes.  — The  length  of  the  spectrum 
varies  with  the  degree  of  dispersion.  It  is  evident  that 
the  greater  the  dispersion,  the  more  the  dark  lines  will  be 
spread  out  lengthwise  in  the  spectrum,  and  separated  from 
each  other.  It  is  as  if  magnifying  power  were  increased. 
Consequently  the  higher  the  dispersion,  the  greater  the 
number  of  dark  lines  which  can  be  seen  and  photographed. 

When  a  greater  degree  of  dispersion  is  required  than  one  prism  will 
produce,  it  is  usual  to  employ  an  arrangement  of  many  prisms,  as  shown 

in  the  figure.  Light  comes 
from  the  object  glass  of  the 
collimator  on  the  left,  and 
passes  round  through  several 
prisms  successively,  disper- 
sion becoming  greater  and 
greater,  as  indicated  by  the 
gradually  widening  white 
band,  which  finally  passes 
into  the  observing  telescope 
on  the  right.  When  prisms 
and  their  accompanying 
small  telescopes  are  rigidly 
secured  to  the  great  tube  in 
place  of  the  eyepiece  ordi- 
narily used  with  it,  such  a 
combination  of  the  two  in- 
struments is  often  called  a 
telespectroscope.  In  the 
diffraction  spectroscope,  in- 

A  High  Power  Prism  Spectroscope  crease    Qf   pQwer  jg   obtained 

by  passing  to  the  spectrum  of  a  higher  order,  which  is  obtained  by 
tilting  the  grating  at  an  angle  suitable  to  the  order  (second,  third,  or 
fourth)  of  spectrum  desired.  In  all  cases,  the  higher  the  degree  of 
dispersion,  the  fainter  becomes  the  spectrum  in  every  part.  So  that 
a  practical  limit  is  soon  reached. 


Photographing  the  Suns  Spectrum          275 


Slit  and  the  Comparison  Prism 


Principles  of  Spectrum  Analysis.  —  In  1858  Kirchhoff 
reduced  to  the  following  compact  and  comprehensive  form 
the  three  principles  underlying  the  theory  of  spectrum 
analysis:  (i)  Solid  and  liquid  bodies,  also  gases  under 
high  pressure,  give,  when  incandescent,  a  continuous  spec- 
trum. (2)  Gases  under  low 
pressure  give  a  discontinuous 
spectrum,  crossed  by  bright 
lines  whose  number  and  posi- 
tion in  the  spectrum  differ 
according  to  the  substances 
vaporized.  (3)  When  white 
light  passes  through  a  gas, 

this  medium  absorbs  rays  of  identical  wave  length  with 
those  composing  its  own  bright-line  spectrum.  Therefore 
dark  lines  or  bands  exactly  replace  the  characteristic  bright 
lines  in  the  spectrum  of  the  gas  itself.  This  principle, 
theoretically  correct,  is  easily  illustrated  and  verified  ex- 
perimentally. These  three  fundamental  principles  fully 
account  for  the  discontinuous  spectrum  of  the  sun,  and 
the  multitude  of  dark  Fraunhofer  lines  which  cross  it. 

Photographing  the  Sun's  Spectrum.  —  The  principles  of  spectrum 
analysis  just  enunciated  indicate  clearly  how  to  ascertain  the  elements 
composing  the  sun.  The  process  is  one  of  map- 
ping or  photographing  the  lines  in  the  solar  spec- 
trum, and  alongside  of  it  in  succession  the  spectra 
of  terrestrial  elements  whose  existence  in  the  sun 
is  suspected.  This  is  effected  by  means  of  the 
comparison  prism,  ab,  shown  above.  It  covers  part 
of  the  slit,  in.  Sun's  rays  come  from  B,  pass  intc 
the  comparison  prism,  are  totally  reflected,  and  pass 
through  the  slit  (downward  in  the  adjacent  figure). 
Thus  they  appear  to  come  from  A,  the  same  as  rays 
from  the  vaporized  substance  under  examination; 
and  as  both  sets  of  rays  then  make  the  optical  circuit 
of  the  spectroscope  side  by  side,  the  field  of  view  embraces  solar 
spectrum  and  spectrum  of  the  terrestrial  substance,  also  side  by 


Course  of  Rays  in 
Comparison  Prism 


276 


The  Sun 


side.  Direct  comparison  line  for  line  is  thereby  greatly  facilitated. 
Rowland  of  Baltimore  and  Higgs  of  Liverpool  have  achieved  very 
marked  success  in  photographing  the  sun's  spectrum.  The  next 
illustration  on  this  page  shows  a  very  small  part  of  that  spectrum, 
known  as  the  '  Great  G  group,1  highly  amplified,  from  a  photograph 


Ul.iJiiJJ.iiilJ  ill;   lilt,  L,;    :  I  Hill    ill  fc  Illltllllii 

Great  G  Group  of  Solar  Spectrum  (photographed  by  Higgs) 

by  the  latter.  These  lines  are  in  the  indigo.  Many  hundreds  of  the 
dark  lines  in  the  sun's  spectrum  are  caused  by  absorption  in  our 
atmosphere.  They  are  called  telluric  lines,  and  variation  in  their 
number  and  intensity  affords  an  excellent  method  of  finding  the 
amount  of  aqueous  vapor  in  the  atmosphere,  as  Jewell  and  others 
have  shown. 

Elements  already  recognized  in  the  Sun.  —  This  process 
of  comparison  of  the  solar  spectrum  with  spectra  of  terres- 
trial elements  has  been  carried  so  far  that  about  40  of  these 
substances  are  now  known  to  exist  in  the  sun.  Among 
them  are  (according  to  Rowland  and  others) :  — 


(Al)    Aluminium 
(Cd)  Cadmium 
(Ca)  Calcium 
(C)     Carbon 
(Cr)    Chromium 
(Co)  Cobalt 
(Cu)   Copper 

(H)     Hydrogen 
(Fe)     Iron 
(Mg)    Magnesium 
(Mn)   Manganese 
(Ni)     Nickel 
(Sc)     Scandium 
(Si)      Silicon 

(Ag)  Silver 
(Na)  Sodium 
(Ti)    Titanium 
(V)     Vanadium 
(Y)     Yttrium 
(Zn)    Zinc 
(Zr)     Zirconium 

The  certainty  with  which  an  element  is  recognized  de- 
pends upon  two  things :  (a)  the  number  of  coincidences  of 
spectral  lines,  (b)  the  intensity  of  the  lines.  Calcium  ranks 
first  in  intensity,  but  iron  has  by  far  the  greatest  number 
of  lines,  with  more  than  2000  coincidences.  All  told,  it 
may  be  said  that  iron,  calcium,  hydrogen,  nickel,  and  sodium 


The  Bolometer 


277 


are  the  most  strongly  indicated.  Runge  has  found  certain 
evidence  of  oxygen  in  the  sun.  Chlorine  and  nitrogen, 
abundant  elements  on  the  earth,  and  gold,  mercury,  phos- 
phorus, and  sulphur  are  not  indicated  in  the  solar  spectrum. 
Sun-spot  Spectrum.  —  If  the  spectrum  of  the  sun  itself 
is  complicated,  that  of  a  spot  is  even  more  so.  In  it  are 
multitudes  of  fine  dark  lines,  indicating  a  greater  degree 
of  gaseous  absorption  than  prevails  on  the  sun  generally. 

A  few  of  the  Fraunhofer  lines  in  the  ordinary  solar  spectrum  are 
not  only  deepened  in  intensity,  but  broadened  out  in  the  spot  spectrum, 
as  shown  in  the  illustration.  The  dark  belt  running  lengthwise  through 
the  middle  is  the 
spectrum  of  the 
umbra,  and  above 
and  below  it  are 
spectra  of  both 
sides  of  the  pen- 
umbra, much  less 
dark.  Thickening 
of  the  lines  is  most 
marked  in  the  um- 
bra, and  gradually 
diminishes  on  both 
sides  to  the  edges 
of  the  penumbra. 
Not  infrequently 

these  heavily  thickened  lines  are  pierced  in  the  middle  by  a  narrow 
bright  line,  called  a  <  double  reversal.1  Always  this  is  true  of  the  H 
and  K  bands  in  the  spot  spectrum.  Spectra  of  many  spots  strengthen 
the  view  that  the  spots  are  themselves  depressions.  Occasionally  it 
happens  that  there  is  a  violent  motion,  either  toward  or  from  us,  of  the 
gases  above  a  spot ;  this  produces  in  the  spectrum  a  marked  distortion 
or  branching  of  the  dark  lines.  By  measuring  the  amount  and  direc- 
tion of  this  distortion,  it  can  be  calculated  whether  the  gases  were 
rushing  toward  or  from  us,  and  at  what  speed.  On  rare  occasions 
these  velocities  have  been  as  great  as  200  or  even  300  miles  per  second. 
The  simple  principle  by  which  this  is  done  is  known  as  '  Doppler's 
principle.'  It  is  explained  on  page  432. 

The  Bolometer.  —  With  rise  in  its  temperature,  a  metal  becomes  a 
poorer  conductor  of  electricity;  with  loss  of  heat,  it  conducts  elec- 
tricity better.  Iron  at  300°  below  centigrade  zero  is  nearly  as  perfect 


Thickened  Lines  of  Spot  Spectrum 


278  The  Sun 

an  electrical  conductor  as  copper  at  ordinary  temperatures.  Upon  the 
application  of  this  important  relation  depends  the  principle  of  tne 
bolometer.  Its  distinctive  feature  is  a  tiny  strip  of  platinum  leaf,  look-^ 
ing  much  like  a  fine  hair  or  coarse  spiderweb.  It  is  about  \  inch  long, 
•sfa  inch  broad,  and  so  thin  that  a  pile  of  25,000  such  strips  would  be 
only  an  inch  high.  This  bolometer  strip  is  connected  into  an  electric 
circuit,  and  it  is  then  carried  slowly  along  the  region  of  the  infra-red 
spectrum,  and  kept  parallel  to  the  Fraunhofer  lines.  So  sensitive  is 
this  instrument  that  the  inconceivably  slight  change  of  temperature 
of  only  the  one-millionth  of  a  degree  of  the  centigrade  scale  may  be 
indicated. 

Infra-red  of  the  Solar  Spectrum.  —  Beneath  and  beyond 
the  red  in  the  solar  spectrum  is  an  extensive  region  of  dark 
bands  wholly  invisible  to  the  human  eye ;  nevertheless  it 
has  been  photographed  with  certainty.  But  the  actinic  or 


Invisible 
Invisible  Heat  Spectrum  (photographed  by  Langley) 

chemical  intensity  is  very  feeble  in  this  region,  so  that  it  is 
difficult  to  photograph  directly.  Langley,  by  means  of  an 
ingenious  automatic  process,  in  conjunction  with  his  bo- 
lometer, or  spectro-bolometer,  has  photographed  the  sun's 
heat  spectrum  in  a  form  comparable  with  the  normal  spec- 
trum. The  above  illustration  represents  its  dark  bands. 
The  length  of  the  invisible  spectrum  is  extraordinary,  being 
10  times  that  of  the  sun's  luminous  spectrum,  which  would 
be  represented  on  the  same  scale  by  a  trifle  more  than  the 
diameter  of  a  lead  pencil  to  the  left  of  A. 

Ultra-violet  of  the  Solar  Spectrum. —  When  we  pass  to  higher  re- 
gions of  the  sun's  spectrum  known  as  the  violet,  the  light  intensity  is 
rapidly  weakened,  so  that  the  lines  become  invisible  to  the  eye.  Pho- 
tographs of  this  region  can,  however,  be  taken,  because  the  chemical 
intensity  is  great.  In  this  manner,  photographic  maps  of  the  invisible 


Absorption  by  Solar  Atmosphere  279 


ultra-violet  spectrum  were  made  by  Cornu,  and  their  length  is  many 
times  that  of  the  visible  spectrum.  Just  where  the  ultra-violet  spectrum 
really  ends  is  not  known,  as  the  farther  region  of  it  appears  to  termi- 
nate abruptly  in  consequence  of  absorption  by  the  earth's  atmosphere. 

How  to  distinguish  True  Solar  from  Telluric  Lines.  —  Dark  lines  in 
the  solar  spectrum  being  produced  by  absorption  in  our  own  atmos- 
phere, as  well  as  in  that  of  the  sun,  it  is  important  to  have  some  method 
of  distinguishing  between  them.  One  way  is  as  follows,  employing 
Doppler's  principle.  Arrange  the  spectroscope  so  that  sunlight  may 
fall  upon  a  small  oscillating  mirror,  which  reflects  into  the  slit  alter- 
nately rays  from  the  east  and  the  west  limb.  On  account  of  the  sun's 
rotation,  the  east  limb  is  coming  toward  us ;  so  the  truly  solar  lines 
in  its  spectrum  will  be  displaced  toward  the  violet.  Similarly,  those 
of  the  west  limb  will  lie  toward  the  red,  because  that  limb  is  going 
from  us.  As  the  mirror  oscillates,  Fraunhofer  lines  caused  by  solar 
absorption  will  themselves  vibrate  forth  and  back,  as  if  the  spectrum 
were  being  shaken  ;  but  dark  lines  due  to  absorption  by  our  atmosphere 
will  remain  all  the  time  immovable  —  a  method  due  to  Cornu. 

Absorption  by  Solar  Atmosphere. — Absorption  by  the 
sun's  own  atmosphere  not  only  reduces  the  amount  of  sun- 
light received  by  the  earth,  but  also  changes  its  character. 
Langley    has    ascertained 
that    if    this     atmosphere 
possessed     no  .   absorbing 
property,    the    sun    would 
shine   two   or  three  times 
brighter  than  it  now  does, 
and    with    a    bluish    color 
resembling     that    of     the 
electric  arc  light. 

Project  the  sun's  entire  image 
on  a  screen,  as  if  looking  for 
spots ;  quite  marked  is  the  dif- 
ference between  the  intensity 
of  light  at  center  of  disk  and 
at  its  edge.  Try  the  experi- 
ment illustrated  in  the  adjacent 
picture.  Where  the  sun's  image  fills  upon  a  screen,  puncture  it 
in  two  places,  so  that  two  pencils  of  sunlight  may  pass  through  and 


Solar  Disk  much  brighter  at  the  Center 
than  near  the  Limb 


280  The  Sun 

fall  upon  a  second  screen.  As  one  of  these  comes  from  the  edge  of  the 
solar  disk,  and  the  other  from  its  center,  their  difference  in  intensity  is 
rendered  very  obvious.  It  can  be  measured  by  a  photometer.  The 
sun's  disk  is  only  two  fifths  as  bright  close  to  the  limb  as  at  the  center. 
This  comparison  relates  only  to  rays  by  which  we  see  in  the  red  and 
yellow  part  of  the  spectrum.  If  a  similar  comparison  is  made  for  blue 
and  violet  rays,  by  which  the  photographic  plate  is  affected,  absorp- 
tion is  very  much  greater ;  photographically,  the  light  at  the  edge  of 
the  sun's  disk  is  only  one  seventh  as  strong  as  at  the  center.  This 
renders  it  difficult  to  photograph  the  entire  sun  with  but  a  single  expo- 
sure, so  as  to  show  an  even  disk ;  for  if  the  exposure  is  short  enough 
for  the  bright  center,  the  image  is  very  faint  at  the  border. 

The  Chromosphere  and  Prominences.  —  Above  and  every- 
where surrounding  the  sun's  bright  surface  is  a  gaseous 
envelope,  called  the  chromosphere.  First  seen  during  the 
total  solar  eclipses  of  1605  and  1706  as  an  irregular  rose- 
tinted  fringe,  analysis  of  the  light  shows  that  it  is  mainly 
composed  of  glowing  hydrogen,  although  sodium,  magne- 
sium, and  other  metals  are  present.  Depth  of  the  chromo- 
sphere is  not  everywhere  the  same,  and  it  varies  between 
5000  and  10,000  miles.  Projected  up  through  the  chromo- 
sphere, but  connected  with  it,  are  the  fiery-red,  cloud- 
shaped  prominences  or  protuberances.  It  was  first  found 
that  they  are  not  lunar  appendages,  because  the  moon  was 
seen  to  pass  gradually  over  them  during  a  total  eclipse. 
Afterward  the  spectroscope  verified  this  inference  by 
showing  that  their  light  is  due  chiefly  to  incandescent 
hydrogen.  Also  there  are  the  H  and  K  lines,  indicating 
vapor  of  calcium ;  and  a  bright  yellow  line,  Z?3,  due  to 
helium,  an  element  not  known  on  the  earth  till  discovered 
in  1895  by  Ramsay,  but  long  known  by  its  line  to 
exist  in  the  sun,  whence  its  name.  It  is  a  very  light  gas 
obtained  from  a  mineral  called  uraninite.  The  promi- 
nences are  now  photographed  every  clear  day  by  means 
of  the  spectroheliograph.  This  ingenious  instrument  fur- 
nishes in  a  few  seconds  a  complete  picture  of  the  promi- 


The  Spectroheliograph 


281 


nences  all  the  way  round  the  sun's  limb,  which  by  the 
older  methods  of  observing  the  protuberances  piecemeal 
would  require  hours  to  make.  Prominences  cannot  be 
observed  by  the  telescope  alone  without  the  spectroscope, 
except  during  eclipses  of  the  sun.  They  are  most  abun- 
dant over  the  sun's  equator  and  the  zones  of  greatest 
spottedness  on  either  side  of  it ;  but  while  spots  are  never 
seen  beyond  latitude 
45°,  prominences 
have  been  observed 
in  all  latitudes,  even 
up  to  the  sun's  poles. 
They  are  least  nu- 
merous about  latitude 

65°. 

The  Spectroheliograph. 
—  Young  in  1870  was  the 
first  to  photograph  a  solar 
prominence.  No  very 
decided  success  was  at- 
tained until  about  20  years 
afterwards,  by  the  use  of 
sensitive  dry  plates  ex- 
posed in  the  spectroscope. 
By  the  addition  of  suit- 
able accessory  apparatus — 
mainly  a  second  slit  with 
the  means  of  moving 
both  slits  automatically,  — 
the  spectroscope  is  con- 
verted into  a  Spectrohelio- 
graph. This  remarkable 

instrument,  as  devised  and  employed  by  Hale  and  built  by  Brashear, 
is  depicted  in  the  above  illustration.  On  pages  282  and  283  are  photo- 
graphs of  two  large  prominences,  taken  with  the  Spectroheliograph. 
By  occulting  the  sun's  disk  behind  an  opaque  circular  screen  just  large 
enough  to  cover  it  and  permit  the  light  of  the  chromosphere  to  graze  its 
edge,  all  the  prominences  and  the  entire  chromosphere  are  photo- 
graphed at  once.  Records  of  this  character  are  now  rapidly  accumu- 


The  Spectroheliograph  (Hale) 


282  The  Sun 

lating,  day  by  day.  Having  made  exposure  for  chromosphere  and 
prominences,  if  the  occulting  disk  is  then  removed,  and  the  slit  made 
to  travel  swiftly  back,  the  photograph  comes  out  as  already  shown  on 
page  269,  in  which  the  faculae  are  especially  prominent.  A  similar  in- 
strument with  which  almost  identical  results  are  obtained  has  been 
devised  and  used  by  Deslandres  of  the  Paris  Observatory. 

Classification  of  the  Prominences.  —  The  number,  height, 
and  variety  of  forms  of  prominences  are  very  great. 
They  are  seen  at  every  part  of  the  sun's  limb,  being  most 
abundant  in  an  equatorial  zone  about  90°  in  breadth.  Be- 


Eruptive  Prominence  (25th  March,   1895).     Spectroheliogram  by  Hale 

yond  latitude  45°  north  and  south,  there  is  a  marked  fall- 
ing off  to  about  65°,  followed  by  a  renewed  frequency  in 
the  region  of  both  poles.  The  average  height  of  the 
prominences  is  about  25,000  miles,  or  about  three  times 
the  diameter  of  the  earth.  Occasionally  prominences  start 
up  to  a  height  exceeding  100,000  miles,  as  indicated  on  the 
colored  plate  at  page  10;  and  the  greatest  heights  ever 
observed  were  300,000  and  350,000  miles,  approaching  half 
the  sun's  diameter.  The  latter  was  observed  by  Young, 
7th  October,  1880.  Frequently  protuberances  are  promi- 
nently developed  at  exactly  opposite  points  on  the  sun's 


The  Envelopes  of  the  Sun  283 

disk.  As  to  form  and  structure,  prominences  are  divided 
into  two  classes  :  eruptive  or  metallic,  and  cloud-like,  qui- 
escent prominences  of  hydrogen  (see  plate  v).  The 
former  generally  appear  like  brilliant  jets,  or  separate 
filaments,  varying  rapidly  in  form  and  brightness.  The 
spectrum  of  eruptive  prominences  shows  the  presence  of  a 
large  number  of  metallic  vapors.  For  the  most  part  they 
are  observed  near  the  spot  zones  only,  and  never  very  near 


Quiescent  Prominence  (3d  July,    1894).     Spectroheliogram  by  Hale 

the  poles  of  the  sun.  The  velocity  of  detached  filaments 
often  exceeds  100  miles  in  a  second  of  time,  and  on  rare 
occasions  it  is  four  or  five  times  as  swift.  Frequently 
prominences  form  exactly  over  spots.  Quiescent  ones  are 
usually  of  enormous  size  laterally,  and  in  appearance  they 
are  a  close  counterpart  of  terrestrial  cirrus  and  stratus 
clouds.  Changes  in  them  are  not  as  a  rule  rapid,  and  near 
the  sun's  poles  they  have  been  known  to  last  nearly  a  month 
without  much  change  of  form.  Tacchini  of  Rome  has  been 
the  most  persistent  observer  of  prominences. 

The  Envelopes  of  the  Sun. —  The  interior  of  the  sun  is 


284 


The  Sun 


probably  composed  of  gases,  in  a  state  quite  unfamiliar  to 
us,  on  account  of  intense  heat  and  compression  due  to  solar 
gravity.  In  consistency  they  may  perhaps  resemble  tar  or 
pitch.  A  series  of  layers,  or  shells,  or  atmospheres  sur- 
round the  main  body  of  the  sun.  The  illustration  has  been 
conceived  by  Trouvelot  to  show  the  condition  of  things 
at  the  sun's  surface  and  just  beneath  it.  Although  the 
view  is  a  theoretical  one,  it  has  been  made  up  from  a  rea- 


Atmosphere  of  the  Sun  in  Ideal  Section  (from  Bulletin  Astronomique) 

sonable  interpretation  of  all  the  facts.  Proceeding  from 
the  outside  inward,  we  meet  first  the  very  thin  shell  called 
the  chromosphere,  probably  about  5006  miles  in  thickness. 
Immediately  underneath  is  the  photosphere,  made  up  of 
filaments  due  to  the  condensation  of  metallic  vapors.  The 
outer  ends  of  these  filaments  form  the  granular  structures 
which  we  see  upon  the  sun  generally,  and  their  light  shines 
through  the  chromosphere.  Between  them  and  the  chromo- 
sphere is  an  envelope  thinner  still,  perhaps  1000  miles  in 
thickness,  and  represented  by  the  darker  shaded  upper 
side  of  the  photosphere.  It  is  called  the  reversing  layer. 
In  this  gaseous  envelope  takes  place  that  absorption  which 
gives  rise  to  the  Fraunhofer  lines.  Where  undisturbed  by 
eruptions  from  beneath,  the  filaments  of  the  photosphere 
are  radial ;  but  where  such  eruptions  take  place,  producing 
under  certain  conditions  the  spots,  these  filaments  are 


Light  and  Brilliance  of  the  Sun          285 

swept  out  of  their  normal  vertical  lines,  as  shown,  form- 
ing the  penumbra  of  the  spot  as  seen  from  our  point  of 
view.  From  the  outer  surface  of  the  body  of  the  sun 
proper  (which  we  never  see)  rise  vapors  of  hydrogen  and 
various  metals  of  which  the  sun  is  composed.  Numbers 
of  these  eruptive  columns  are  shown.  They  are  spread 
into  masses  of  cloud-like  forms  composed  of  metallic  vapors 
underneath  the  photosphere.  As  these  columns  grow 
in  number  and  stress  becomes  more  and  more  intense, 
outbursts  through  the  photospheric  shell  take  place,  giv- 
ing rise  to  phenomena  known  as  sun  spots  and  protuber- 
ances. Naturally  such  eruptions  would  be  more  violent  at 
one  time  than  at  another,  and  we  might  expect  them  to 
occur  periodically,  just  as  we  observe  the  spots  actually 
do.  Still  above  the  chromosphere  and  prominences  is  the 
corona,  not  an  atmosphere,  properly  speaking,  but  a  lumi- 
nous appendage  of  the  sun  (not  shown  in  this  illustration) 
whose  light  is  of  a  complex  character,  and  about  which 
relatively  little  is  known,  because  it  can  be  seen  only  dur- 
ing total  eclipses  of  the  sun.  Illustrations  of  it  are  given 
in  the  next  chapter,  with  theories  of  its  constitution. 

Light  and  Brilliance  of  the  Sun.  —  It  is  not  easy  to  con- 
vey, in  words  or  figures,  any  idea  of  the  amount  of  light 
given  out  by  the  sun,  since  the  figures  expressed  in  '  candle 
power,'  or  in  terms  of  the  ordinary  gas  burner,  or  even  the 
arc  light,  are  so  enormous  as  really  to  be  beyond  our  com- 
prehension. Indeed,  any  of  these  artificial  illuminations, 
even  the  most  brilliant  electric  light,  if  placed  between  the 
eye  and  the  sun,  seems  black  by  comparison.  The  sun  is 
nearly  four  times  brighter  than  the  brightest  part  of  the 
electric  arc.  By  an  experiment  at  a  steel  works  in  Penn- 
sylvania, Langley  compared  direct  sunlight  with  the  blind- 
ing stream  of  molten  metal  from  a  Bessemer  converter  ;  and 
although  absolutely  dazzling  in  its  brightness,  sunlight 


286  The  Sun 

was  found  to  be  more  than  5000  times  brighter.  The 
amount  of  light  received  from  the  sun  is  equal  to  that  from 
600,000  full  moons. 

The  Sun's  Heat  at  the  Earth.  —  Although  difficult  to  give 
an  idea  of  the  sun's  light,  much  more  so  is  it  to  convey  an 
adequate  notion  of  his  enormous  heat.  So  great  is  that 
heat,  even  at  our  vast  distance  from  the  sun,  that  it  exceeds 
intelligible  calculation.  The  unit  of  heat  is  called  the  calorie, 
and  it  signifies  the  amount  of  heat  required  to  raise  the  tem- 
perature of  a  kilogram  of  water  one  degree  of  the  centi- 
grade scale.  The  number  of  calories  received  each  minute 
upon  a  square  meter  of  the  earth's  surface  has  been  re- 
peatedly measured,  and  found  to  be  30,  neglecting  the 
considerable  portion  which  is  absorbed  by  our  atmosphere. 
No  variation  in  this  amount  has  yet  been  detected  ;  so  that 
30  calories  per  square  meter  per  minute  is  termed  the  solar 
constant.  With  the  sun  in  the  zenith,  his  heat  is  powerful 
enough  to  melt  annually  a  layer  of  ice  on  the  earth  nearly 
170  feet  in  thickness.  Or  if  we  measure  off  a  space  five 
feet  square,  the  energy  of  the  sun's  rays,  when  falling  ver- 
tically upon  it,  is  equivalent  to  one  horse  power,  or  the 
work  of  about  five  men.  Upon  the  deck  of  a  steamer  on 
tropical  oceans  there  falls  enough  heat  to  propel  it  at  about 
10  knots,  if  only  that  heat  could  be  fully  utilized.  Several 
attempts  have  been  made  to  employ  solar  heat  directly  for 
industrial  purposes,  and  Ericsson,  the  great  Swedish  engi- 
neer, and  Mouchot  built  solar  engines.  The  sun's  gaseous 
envelope,  too,  absorbs  heat.  Frost  has  shown  that  all 
parts  of  the  disk  radiate  uniformly,  and  that  we  should 
receive  1.7  times  more  heat,  if  the  solar  atmosphere  were 
removed. 

The  Sun's  Heat  at  the  Sun. — The  intensity  of  heat, 
like  that  of  light,  decreases  as  the  square  of  the  distance 
from  the  radiating  body  increases.  Therefore,  the  amount 


Maintenance  of  Solar  Heat  287 

^*ss2^CAL  I F  Qfi^}^^ 

of  heat  radiated  by  a  given  area  of  the  sun's  surface  must 
be  about  46,000  times  greater  than  that  received  by  an 
equal  area  at  the  distance  of  the  earth. 

One  square  meter  of  that  surface-  radiates  heat  enough  to  generate 
more  than  100,000  horse  power,  continuously,  night  and  day.  Imagine 
a  solid  cylinder  of  ice,  nearly  three  miles  in  diameter  and  as  long  as  the 
distance  from  the  earth  to  the  sun.  The  sun  emits  heat  sufficient  to 
melt  this  vast  column  in  a  single  second  of  time ;  in  eight  seconds  it 
would  be  converted  into  steam.  Were  the  sun  no  farther  from  us  than 
the  moon,  not  only  would  his  vast  globe  fill  the  entire  sky,  but  his  over- 
powering heat  would  vaporize  the  oceans,  and  speedily  melt  the  solid 
earth  itself.  To  investigate  this  inconceivable  outlay  of  heat,  to  deter- 
mine the  laws  of  its  radiation  and  its  effects  upon  the  earth,  and  to 
theorize  upon  the  method  by  which  this  heat  is  maintained,  are  among 
the  most  important  and  practical  problems  of  the  astronomy  of  the 
present  day.  Whether  the  amount  of  heat  given  out  by  the  sun  is  a 
constant  quantity,  or  whether  it  varies  from  year  to  year  or  from  cen- 
tury to  century,  is  not  yet  determined.  The  temperature  of  the  sun  is 
very  difficult  to  ascertain.  Widely  different  estimates  have  been  made. 
Probably  16,000°  to  18,000°  Fahrenheit  is  near  the  truth.  But  no 
artificial  heat  exceeds  4000°  F. 

How  the  Sun's  Heat  is  maintained. — The  sun's  heat 
cannot  be  maintained  by  the  combustion  of  carbon,  for 
although  the  vast  globe  were  solid  anthracite,  in  less  than 
5000  years  it  would  be  burned  to  a  cinder.  Heat,  we 
know,  may  result  from  sudden  impact,  as  the  collision 
of  bodies.  According  to  one  theory,  the  sun's  heat  may  be 
maintained  by  the  impact  of  falling  meteoric  matter,  and 
very  probably  this  accounts  for  a  small  fraction  ;  but  in 
order  that  all  the  heat  should  be  produced  in  this  manner, 
an  amount  of  matter  equal  to  a  hundredth  part  of  the 
earth's  mass  would  have  to  fall  upon  the  sun  each  year 
from  the  present  distance  of  the  earth.  This  seems  very 
unlikely.  Only  one  possible  explanation  remains :  if  the 
sun  is  contracting  upon  himself,  no  matter  how  slowly, 
gases  composing  his  volume  must  generate  heat  in  the 
process.  The  eminent  German  physicist,  von  Helmholtz 


288  The  Sun 

first  proposed  this  theory,  nearly  a  half  century  ago,  and 
it  is  now  universally  accepted.  So  enormous  is  the  sun 
that  the  actual  shortening  of  his  diameter  (the  only  dimen- 
sion we  can  measure)  need  take  place  but  very  slowly.  In 
fact,  a  contraction  of  only  six  miles  per  century  would  fully 
account  for  all  the  heat  given  out  by  the  sun.  But  six 
miles  would  subtend  an  angle  of  only  y1^  of  a  second 
of  arc  at  the  sun,  and  this  is  very  near  the  limit  of 
measurement  with  the  most  refined  instruments.  So  it  is 
evident  that  many  centuries  must  elapse  before  observa- 
tion can  verify  this  theory. 

The  Past  and  Future  of  the  Sun.  —  Accepting  the 
theory  that  the  sun's  heat  is  maintained  by  gradual 
shrinkage  of  his  volume,  he  must  have  been  vastly  larger 
in  the  remote  past,  and  he  will  become  very  much  reduced 
in  size  in  the  distant  future.  If  we  assume  the  rate  of 
contraction  to  remain  unchanged  through  indefinite  ages, 
it  is  possible  to  calculate  that  the  earth  has  been  receiving 
heat  from  the  sun  about  20,000,000  years  in  the  past ; 
also,  that  in  the  next  5,000,000  years,  he  will  have  shrunk 
to  one  half  his  present  diameter.  For  5,000,000  years  addi- 
tional, he  might  continue  to  emit  heat  sufficient  to  main- 
tain certain  types  of  life  on  our  earth.  A  vast  period  of 
30,000,000  to  40,000,000  years,  then,  may  be  regarded  as 
the  likely  duration,  or  life  period,  of  the  solar  system,  from 
origin  to  end.  Their  heat  all  lost  by  radiation,  the  sun 
and  his  family  of  planets  might  continue  their  journey 
through  interstellar  space  as  inert  matter  for  additional 
and  indefinite  millions  of  years. 


CHAPTER   XII 

ECLIPSES   OF   SUN   AND   MOON 

IN  earliest  ages,  every  natural  event  was  a  mystery. 
Day  and  night,  summer  and  winter,  and  the  most 
ordinary  occurrences  filled  whole  nations  with  wonder, 
and  fantastic  explanations  were  given  of  the  simplest 
natural  phenomena.  But  when  anything  happened  so 
strange,  and  even  frightful,  as  the  total  darkening  of  the 
sun  in  the  daytime,  it  is  scarcely  matter  for  surprise  that 
fear  and  superstition  ran  riot.  Some  nations  believed 
that  a  vast  monster  was  devouring  the  friendly  sun,  and 
barbarous  noises  were  made  to  frighten  him  away.  For 
ages  the  sun  was  an  object  of  worship,  and  it  was  but 
natural  that  his  darkening,  apparently  inexplicable,  should 
have  brought  consternation  to  all  beholders.  Among 
uncivilized  peoples,  the  ancient  view  regarding  eclipses 
prevails  to  the  present  day. 

Remarkable  Ancient  Eclipses.  —  The  earliest  mentioned  solar  eclipse 
took  place  in  B.C.  776,  and  is  recorded  in  the  Chinese  annals.  During 
the  next  hundred  years  several  eclipses  were  recorded  on  Assyrian  tab- 
lets or  monuments.  On  28th  May,  B.C.  585,  took  place  a  total  eclipse 
of  the  sun,  said  to  have  been  predicted  by  Thales,  which  terminated  a 
battle  between  the  Medes  and  Lydians.  This  eclipse  has  helped  to 
fix  the  chronology  of  this  epoch.  So,  too,  a  like  eclipse,  3d  August, 
B.C.  431,  has  established  the  epoch  of  the  first  year  of  the  Peloponnesian 
war;  and  the  eclipse  of  I5th  August,  B.C.  310,  is  historically  known  as 
'  the  eclipse  of  Agathocles,'  because  it  took  place  the  day  after  he  had 
invaded  the  African  territory  of  the  Carthaginians,  who  had  blockaded 
him  in  Syracuse :  '  the  day  turned  into  night,  and  the  stars  came  out 
everywhere  in  the  sky.'  Also  a  few  solar  eclipses  are  connected  with 
TODD'S  ASTRON.  —  19  289 


290 


Eclipses  of  Sun  and  Moon 


LTHESUNJ 


events  in  Roman  history.  The  first  historic  reference  to  the  corona, 
or  halo  of  silvery  light  which  seems  to  encircle  the  dark  eclipsing  moon, 
occurs  in  Plutarch's  description  of  the  total  eclipse  of  2oth  March,  A.D. 
71.  Although  it  must  have  been  frequently  seen,  there  is  no  subsequent 
mention  of  it  till  near  the  end  of  the  i6th  century.  The  few  eclipses 
recorded  in  this  long  interval  have  little  value,  scientific  or  otherwise, 
except  as  they  have  helped  modern  astronomers  to  ascertain  the  motion 
of  the  moon. 

The  Cause  of  Solar  Eclipses.  —  Any  opaque  object  inter- 
posed  between  the  eye  and  the  sun  will   cause  a  solar 

eclipse ;    and   it  will 

be  total  provided  the 
angle  filled  by  the 
object  is  at  least  as 
great  as  that  which 
the  sun  itself  sub- 
tends ;  that  is,  about 
one  half  a  degree. 
Every  one  recog- 
nizes the  shadow  of 
the  eagle  flying  over 
the  highway,  and  the 
cloud's  dark  shadow 
moving  slowly  across 
the  landscape,  as  pro- 
duced by  the  inter- 
position of  a  dark 
body  between  sun 
and  earth.  To  the 
eager  spectators  on 
the  towers  of  Notre 
Dame,  Paris,  2ist 
October,  1783,  there 

appeared  a  novel  sort  of  solar  eclipse,  caused  by  the  drift- 
ing between  them  and  the  sun  of  the  balloon  in  which 


How  Eclipses  of  Sun  and  Moon  take  Place 


Shadows  of  Heavenly  Bodies 


were  M.  Pilatre  and  the  Marquis 
d'Arlandes.  And  just  as  when  the 
eye  is  placed  below  the  eagle,  or 
behind  the  cloud,  or  beneath  the 
balloon,  an  apparent  but  terrestrial 
eclipse  of  the  sun  is  seen,  just  so 
when  the  moon  comes  round  be- 
tween earth  and  sun  a  real  or  astro- 
nomical eclipse  of  the  sun  takes 
place.  But  the  great  advantage  of 
the  latter  comes  from  the  fact  that 
the  moon,  the  eclipse-producing 
body,  is  very  much  farther  away 
than  cloud,  and  eagle,  and  balloon 
are,  — beyond  the  atmosphere  of  the 
earth,  at  a  distance  relatively  very 
great  and  comparable  with  that  of 
the  sun  itself.  It  is  a  striking  fact 
that  the  sun,  about  400  times  larger 
than  the  moon,  happens  to  be  about 
400  times  farther  away,  so  that  sun 
and  moon  both  appear  to  .be  of 
nearly  the  same  size  in  the  heavens. 
A  slight  variation  of  our  satellite's 
size  or  distance  might  have  made  that 
impressive  phenomenon,  the  sun's 
total  eclipse,  forever  impossible. 

The  Shadows  of  Heavenly  Bodies. 
—  As  every  earthly  object,  when  in 
sunshine,  casts  a  shadow  of  the 
same  general  shape  as  itself,  so  do 
the  celestial  bodies  of  our  solar  sys- 
tem. All  these,  whether  planets  or 
satellites,  are  spherical ;  and  as  they 


291 


050- 


Slender  Shadows  of  Earth 
and  Moon 


292  Eclipses  of  Sun  and  Moon 

are  smaller  than  the  sun,  it  is  evident  that  their  shadows 
are  long,  narrow  cones  stretching  into  space  and  always 
away  from  that  central  luminary.  Evidently,  also,  the 
length  of  such  a  shadow  depends  upon  two  things, — the 
size  of  the  sphere  casting  it,  and  its  distance  from  the 
sun.  The  average  length  of  the  shadow  of  the  earth  is 
857,000  miles;  of  the  moon,  232,000  miles.  Each  is  at 
times  about  g1^  part  longer  or  shorter  than  these  mean 
values,  because  our  distance  from  the  sun  varies  g1^  part 
from  the  mean  distance.  So  far  away  is  the  sun  that  the 
shadows  of  earth  and  moon  are  exceedingly  long  and 
slender.  To  represent  them  in  their  true  proportions  is 
impossible  within  the  limits  of  a  small  page  like  this.  In 
the  illustration  just  given,  however,  attempt  is  made  to 
give  some  idea  of  these  slender  shadows ;  but  even  there 
they  are  drawn  five  times  too  broad  for  their  length.  The 
shadow  cast  by  a  heavenly  body  is  a  cone,  and  is  often 
called  the  umbra,  or  dense  shadow,  because  the  sun's  light 
is  wholly  withdrawn  from  it.  Completely  surrounding  the 
umbra  is  a  less  dense  shadow,  from  which,  as  the  figure 
on  page  290  shows,  the  sun's  light  is  only  partly  excluded. 
This  is  called  the  penumbra ;  and  it  is  a  hollow  frustum 
of  a  cone,  whose  base  is  turned  opposite  to  the  base  of  the 
umbra.  Both  umbra  and  penumbra  sweep  through  space 
with  a  velocity  exceeding  2000  miles  an  hour;  and  they 
trail  eastward  across  our  globe.  The  way  in  which  they 
strike  its  surface  gives  rise  to  different  kinds  of  solar 
eclipse,  known  as  partial,  annular,  and  total. 

True  Proportions  of  Earth's  and  Moon's  Orbits.  —  Even  more  difficult 
is  it  to  represent  the  sizes  and  distances  of  sun,  earth,  and  moon,  in  their 
true  relative  proportions  on  paper.  It  is  easy,  however,  to  exhibit  them 
correctly  in  a  medium-sized  lot.  Cut  out  a  disk  one  foot  in  diameter  to 
represent  the  sun.  Pace  off  107  feet  from  it,  and  there  place  an  ordi- 
nary shot,  TV  inch  in  diameter,  to  represent  the  earth.  At  a  distance  of 
3^  inches  from  the  shot,  place  a  grain  of  sand,  or  a  very  small  shot,  to 


Nodes  of  Lunar  Orbit 


293 


represent  the  moon.     Then  not  only  will  the  sizes  of  sun,  earth,  and 
moon,  be  exhibited  in  true  proportion,  but  the  dimensions  of  earth's  and 
moon's  orbits  will  be  correctly  indicated  on  the 
same  scale.      Every  inch   of  this   scale  corre- 
sponds to  72,000  miles  in  space. 

The  Nodes  of  the  Moon's  Orbit.  -  / 
Once  every  month  — •  that  is,  every  time 
the  moon  comes  to  the  phase  called 
new  —  there  would  be  an  eclipse  of  the 
sun,  were  it  not  that  the  moon's  path 
about  the  earth,  and  that  of  the  earth 
about  the  sun  are  not  in  the  same  plane, 
but  inclined  to  each  other  by  an  angle 
of  5^°.  When  our  satellite  comes  round 
to  conjunction  or  new  moon,  she  usually 
nasses  above  or  below  the  sun  whirh  Sun  not  in  Plane  of  Moon's 

in,    Wni     1    Orbit  — Eclipses  Impossible 

therefore     suffers    no     eclipse.       Two 
opposite  points  on  the  celestial  sphere  where  the  plane  of 
moon's  orbit  crosses  ecliptic  are  called  the  moon's  nodes. 

Indeed,  the  term  ecliptic  had  its 
origin  from  this  condition :  it  is 
the  plane  near  to  which  the  moon 
must  be  in  order  that  eclipses 
shall  be  possible. 

The  figures  should  make  this  clear. 
The  sun  is  where  the  eye  is,  and  the 
disk  held  at  arm's  length  represents  the 
lunar  orbit,  the  earth  being  at  its  center. 
When  held  at  the  side,  with  the  wrist 
bent  forward,  the  moon's  shadow  falls 
far  below  the  earth,  and  an  eclipse  is 
impossible.  Now  carry  the  disk  slowly 
to  the  position  of  the  second  figure, 
gradually  straightening  out  the  wrist, 
and  taking  care  to  keep  plane  of  disk 
always  parallel  to  its  first  position :  moon's  orbit  is  now  seen  edge  on, 
and  when  new  moon  occurs,  an  eclipse  of  the  sun  is  inevitable. 


Sun  in  Plane  of  Moon's  Orbit  — 
Eclipses  Inevitable 


294  Eclipses  of  Sun  and  Moon 

Solar  Ecliptic  Limit.  —  As  a  solar  eclipse  cannot  take  place  unless 
some  part  of  the  moon  overlaps  the  sun's  disk,  it  is  clear  that  the 
apparent  diameters  of  these  two  bodies  must  affect  the  distance  of  the 
sun  from  the  moon's  node,  within  which  an  eclipse  is  possible.  This 
distance  is  called  the  solar  ecliptic  limit,  and  the  figure  illustrates  it  on 
both  sides  of  the  ascending  node.  From  the  new  moon  at  the  center 
to  the  farther  new  moon  on  either  side  is  an  arc  of  the  ecliptic  about 
1 8°  long.  This  is  the  value  of  the  solar  ecliptic  limit.  It  is  not  a  con- 
stant quantity,  but  is  greatest  when  perigee  and  perihelion  occur  at  the 


PARTIAL  ECLIPSE  ANNULAR  OR 

TOTAL  ECLIPSE  PARTIAL  ECLIPSE  NO  ECLIPSE 

IPTIC 


NEW  MOON 

Solar  Ecliptic  Limit,  both  East  and  West  of  Moon's  Ascending  Node 

same  time.  As  our  satellite  may  reach  the  new-moon  phase  at  any 
time  within  this  limit,  and  may  therefore  eclipse  the  sun  at  any  dis- 
tance less  than  18°  from  the  moon's  node,  all  degrees  of  solar  eclipse 
are  possible.  They  will  range  from  the  merest  notch  cut  out  of  the 
sun's  disk  when  he  is  remote  from  the  node,  to  the  central  (annular 
or  total)  eclipse  when  he  is  very  near  the  node. 

Two  Solar  Eclipses  Certain  Every  Year.  —  As  the  solar 
ecliptic  limit  is  18°  on  both  sides  of  the  moon's  node,  it  is 
plain  that  an  eclipse  of  the  sun  of  greater  or  less  magni- 
tude is  inevitable  at  each  node,  every  year.  For  the 
entire  arc  of  possible  eclipse  is  about  36°,  and  the  sun 
requires  nearly  37  days  to  pass  over  it.  If,  therefore,  new 
moon  occurs  just  outside  of  the  limit  west  of  the  node  (as 
on  the  right  in  the  figure  just  given),  in  29^  days  she  will 
have  made  her  entire  circuit  of  the  sky,  and  returned  to 
the  sun.  An  eclipse  (partial)  at  this  new  moon  is  certain, 
because  the  sun  can  have  advanced  only  a  few  degrees 
east  of  the  node,  and  is  well  within  the  limit.  One  solar 
eclipse  is  therefore  certain  at  each  node  every  year. 

If  new  moon  falls  just  within  the  limit  west  of  the  node,  two  partial 
solar  eclipses  are  certain  at  that  node ;  also  two  are  possible  in  like 
manner  at  the  opposite  node.  Even  a  fifth  solar  eclipse  in  a  calendar 


Partial  Solar  Eclipses 


295 


year  may  take  place  in  extreme  cases.  For  if  the  sun  passes  a  node 
about  the  middle  of  January,  causing  two  eclipses  then,  two  may  also 
happen  in  midsummer ;  and  the  westward  motion  of  the  node  makes 
the  sun  come  again  within  the  west  limit  in  the  month  of  December, 
with  a  possibility  of  a  fifth  solar  eclipse  before  the  calendar  year  is  out. 
As  two  lunar  eclipses  also  are  certain  in  this  period,  the  greatest  possi- 
ble number  of  eclipses  in  a  year  is  seven.  But  this  happens  only  once 
in  about  three  centuries,  the  next  occasion  being  the  year  1935.  The 
number  of  eclipses  in  a  year  is  commonly  four  or  five. 

Partial  Solar  Eclipses.  —  When  the  moon  comes  almost 
between  us  and  the  sun,  she  cuts  off  only  a  part  of  the 
solar  light,  and  a  partial  eclipse  takes  place. 


Exposure  of 
the  maximum 
phase  imme- 
diately above 
•was  too  long 
and  the  nega- 
tive was  so- 
larized 


Solar  Eclipse  of  1887  (photographed  in  Tokyo,  Japan) 


This  happens  when  the  sun  is  some  distance  removed  from  the  node 
of  the  lunar  orbit.  The  above  figures,  I  to  14,  show  several  advanc- 
ing and  retreating  stages  of  a  partial  eclipse.  The  degree  of  obscura- 
tion is  often  expressed  by  digits,  a  digit  being  the  twelfth  part  of  the 
sun's  diameter.  When  there  is  a  partial  eclipse,  it  is  only  the  moon's 
penumbra  which  strikes  the  earth,  consequently  the  partial  eclipse  will 
be  visible  in  greater  or  less  degree  from  a  large  area  of  the  earth's  sur- 
face, perhaps  2000  miles  in  breadth,  if  measured  at  right  angles  to  the 
shadow,  but  often  double  that  width  on  the  curving  surface  of  our 


296 


Eclipses  of  Sun  and  Moon 


Annular  Eclipse 


globe.  This  will  be  near  the  north  pole  or  the 
south  pole  according  as  the  center  of  the  moon 
passes  to  the  north  or  south  of  the  center  of  the 
sun.  About  90  partial  eclipses  of  the  sun  occur  in 
a  century. 

Annular  Eclipses.  —  If  the  sun  is  very 
near  the  moon's  node  when  our  satellite 
becomes  new,  clearly  the  moon  must  then 
pass  almost  exactly  between  earth  and 
sun.  If  at  the  same  time  she  is  in  apogee, 
her  apparent  size  is  a  little  less  than  that 
of  the  sun.  Then  her  conical  shadow 
does  not  quite  reach  the  surface  of  the 
earth,  and  a  ring  of  sunlight  is  left,  sur- 
rounding the  dark  moon  completely.  This 

is  called  an   annular  eclipse  because   of   the  annulus,   or 

bright  ring  of  sunlight  still  left  shining. 

Its  greatest  possible  breadth 
is  about  ^  the  sun's  apparent 
diameter.  This  ring  may  last 
nearly  12^  minutes  under  the 
most  favorable  circumstances, 
though  its  average  duration  is 
about  one  third  of  that  inter- 
val. The  illustration  shows  the 
ring  at  five  different  phases. 
Nearly  90  annular  eclipses  of 
the  sun  take  place  every  cen- 
tury. Dates  of  annular  eclipses 
near  the  present  time  are  :  — 

1897,  July  29,  visible  in 
Mexico,  Cuba,  and  Antigua. 

1900,  November  22,  from 
Angola  to  Zambesi  and  West 
Australia. 

No   annular   eclipse   visits 

the    United    States  till    28th 

June,  1908,  when  one  may  be  Ph"  s  of  the  Annulus  freduced  from  a  Daguerreo- 
well  seen  in  Florida.  type  by  Alexander) 


Total  Solar  Eclipses 


297 


Total  Solar  Eclipses.  —  Most  impressive  and  important 
of  all  obscurations  of  heavenly  bodies  is  a  total  eclipse  of 
the  sun.  It  takes  place  when  the  lunar  shadow  actually 
reaches  the  earth  as  in  the  illustration.  While  the  moon 
passes  eastward,  approaching  gradually  the  point  where 
she  is  exactly  between  us  and  the  sun,  steadily  the  dark- 
ness deepens  for  over  an  hour,  as  more  and  more  sun- 
light is  withdrawn.  Then  quite  suddenly  the  darkness  of 
late  twilight  comes  on,  when  the  moon 
reaches  just  the  point  where  she  first  shuts 
off  completely  the  light  of  the  sun.  At 
that  instant,  the  solar  corona  flashes  out, 
and  the  total  eclipse  begins.  The  observer 
is  then  inside  the  umbra,  and  totality  lasts 
only  so  long  as  he  remains  within  it. 
Total  eclipses  are  sometimes  so  dark  that 
observers  need  artificial  light  in  making 
their  records.  In  consequence  of  the  mo- 
tion of  the  moon,  the  tip  of  the  lunar 
shadow,  or  umbra,  makes  a  path  or  trail 
across  the  earth,  and  its  average  breadth 
is  about  90  miles.  The  earth  by  its  rota- 
tion is  carrying  the  observer  eastward  in 
the  same  direction  that  the  shadow  is  going.  If  he  is 
within  the  tropics,  his  own  velocity  is  nearly  half  as  great 
as  that  of  the  shadow,  so  that  it  sweeps  over  him  at  can- 
non-ball speed,  never  less  than  1000  miles  an  hour.  As  an 
average,  the  umbra  will  require  less  than  three  minutes  to 
pass  by  any  one  place,  but  the  extreme  length  of  a  total 
solar  eclipse  is  very  nearly  eight  minutes.  Few  have, 
however,  been  observed  to  exceed  five  minutes  in  duration ; 
and  no  eclipses  closely  approaching  the  maximum  duration 
occur  during  the  next  2\  centuries.  Total  eclipses  occur- 
ring near  the  middle  of  the  year  are  longest,  if  at  the 


Total  Eclipse 


298  Eclipses  of  Sun  and  Moon 

same  time  the  moon  is  near  perigee,  and  their  paths  fall 
within  the  tropics.  Always  after  total  eclipse  is  over,  the 
partial  phase  begins  again,  growing  smaller  and  smaller 
and  the  sun  getting  continually  brighter,  until  last  contact 
when  full  sunlight  has  returned.  Nearly  70  total  eclipses 
of  the  sun  take  place  every  century.  If  the  atmosphere 
is  saturate  with  aqueous  vapor,  weird  color  effects  ensue, 
by  no  means  overdrawn  in  the  frontispiece. 

The  Four  Contacts.  —  As  the  moon  by  her  motion  eastward  overtakes 
the  sun,  an  eclipse  of  the  sun  always  begins  on  the  west  side  of  the 
solar  disk.  First  contact  occurs  just  before  the  dark  moon  is  seen  to 
begin  overlapping  the  sun's  edge  or  limb.  Theoretically  the  absolute 
first  contact  can  never  be  observed ;  because  the  instant  of  true  contact 
has  passed,  a  fraction  of  a  second  before  the  moon's  edge  can  be  seen,, 
First  contact  marks  the  beginning  of  partial  eclipse.  If  the  eclipse  is 
total  or  annular,  a  long  partial  eclipse  precedes  the  total  or  annular  phase. 
At  the  instant  this  partial  eclipse  ends,  the  total  or  annular  eclipse 
begins ;  and  this  is  the  time  when  second  contact  occurs.  Usually 
second  contact  will  follow  first  contact  by  a  little  more  than  an  hour. 
If  the  eclipse  is  total,  second  contact  takes  place  on  the  east  side  of  the 
sun  ;  if  annular,  on  the  west  side.  Following  second  contact,  by  a  very 
few  moments  at  the  most,  comes  third  contact :  in  the  total  eclipse,  it 
occurs  at  the  sun's  west  limb ;  in  the  annular  eclipse,  at  the  east  limb. 
Students  should  represent  the  contacts  by  a  diagram.  Then  from  third 
contact  to  last  contact  is  a  partial  eclipse,  again  a  little  more  than  an 
hour  in  duration  —  the  counterpart  of  the  partial  eclipse  between  first 
and  second  contacts.  Fourth  or  last  contact  takes  place  at  the  instant 
when  the  moon's  dark  body  is  just  leaving  the  sun,  and  the  interval  be- 
tween first  and  fourth  contacts  is  usually  about  3  hours.  If  the  eclipse 
is  but  partial,  only  two  contacts,  first  and  last,  are  possible. 

Young's  Reversing  Layer.  —  According  to  the  principles 
of  spectrum  analysis,  a  gas  under  low  pressure  gives  a 
discontinuous  spectrum  composed  of  characteristic  bright 
lines.  As  the  dark  lines  of  the  solar  spectrum  are  produced 
by  absorption  in  passing  through  the  atmosphere  of  the 
sun,  it  occurred  to  Young  that  a  total  eclipse  afforded  an 
opportunity  to  observe  the  bright-line  spectrum  of  this 
atmosphere  by  itself.  Following  is  his  description  of  this 


The  Solar  Corona  299 

phenomenon,  as  seen  for  the  first  time  in  Spain,  during 
the  total  eclipse  of  1870:  — 

*  As  the  moon  advances,  making  narrower  and  narrower  the  remaining 
sickle  of  the  solar  disk,  the  dark  lines  of  the  spectrum  for  the  most  part 
remain  sensibly  unchanged.  .  .  .  But  the  moment  the  sun  is  hidden, 
through  the  whole  length  of  the  spectrum,  in  the  red,  the  green,  the 
violet,  the  bright  lines  flash  out  by  hundreds  and  thousands,  almost 
startlingly ;  as  suddenly  as  stars  from  a  bursting  rocket  head,  and  as 
evanescent,  for  the  whole  thing  is  over  within  two  or  three  seconds.  The 
layer  seems  to  be  only  something  under  a  thousand  miles  in  thickness.' 
A  like  observation  has  been  made  on  several  occasions,  and  during  the 
totality  of  1896  the  bright  lines  were  successfully  photographed.  This 
stratum  of  the  solar  atmosphere,  known  as  Young's  reversing  layer, 
is  probably  between  500  and  1000  miles  in  thickness. 

The  Solar  Corona.  —  The  corona  is  a  luminous  radiance 
seen  to  surround  the  sun  during  total  eclipses.  The  strong 
illumination  of  our  atmosphere  precludes  our  seeing  it  at 
all  other  times.  The  corona,  as  observed  with  the  tele- 
scope, is  composed  of  a  multitude  of  streamers  or  filaments, 
often  sharply  defined,  and  sometimes  stretching  out  into 
space  from  the  disk  of  the  sun  millions  of  miles  in  length. 
For  the  most  part  these  streamers  are  not  arranged  radially, 
and  often  the  space  between  them  is  dark,  close  down  to 
the  disk  itself.  The  general  light  of  the  corona  averages 
about  three  times  that  of  the  full  moon  ;  but  the  amount  of 
this  light  varies  from  one  eclipse  to  another,  just  as  the 
form  and  dimensions  of  the  streamers  do.  The  coronal 
light,  very  intense  close  to  the  sun,  diminishes  rapidly  out- 
ward from  the  disk,  so  that  the  object  is  a  very  difficult 
one  to  photograph  distinctly  in  every  part  on  a  single 
plate.  The  corona  appears  to  be  at  least  triple ;  there  are 
polar  rays  nearly  straight,  inner  equatorial  rays  sharply 
curved,  and  often  outer  equatorial  streamers,  perhaps  con- 
nected in  origin  with  the  zodiacal  light.  The  last  are  not 
visible  at  every  eclipse,  and  it  is  doubtful  whether  they 


300  Eclipses  of  Sun  and  Moon 

have  ever  been  photographed,  although  repeatedly  seen. 
Recent  photographs  of  the  corona  show  no  variation  in 
form  from  hour  to  hour.  As  yet  no  theory  of  this 
marvelous  object  explains  the  phenomena  satisfactorily. 
Neither  a  magnetic  theory  advanced  by  Bigelow,  nor  a 
mechanical  one  by  Schaeberle,  has  successfully  predicted 
its  general  form.  The  brighter  filaments  may  be  due  to 
electric  discharges.  Total  eclipses  permit  only  a  few 
hours'  advantageous  study  of  the  corona,  in  a  century. 

The  Spectrum  of  the  Corona.  —  Our  slight  knowledge  of 
the  corona  is  for  the  most  part  based  on  evidence  fur- 
nished by  the  spectroscope. 

Its  light  gives  a  faint  continuous  spectrum,  showing  incandescent 
liquid  or  solid  matter ;  and  a  superposed  spectrum  of  numerous  bright 
lines  indicating  luminous  gases,  among  them  hydrogen.  Also,  in  the 
violet  and  ultra-violet  are  numerous  bright  lines.  But  the  characteristic 

line  of  the  coronal  spectrum 
is  a  bright  double  one  in  the 
green,  often  called  the  '1474 
line1  ;  one  component  of  it 
coincides  in  position  with  a 
dark  iron  line  in  the  solar 
spectrum,  and  the  other  is  due 
to  a  supposed  element  called 
*  coronium '  existing  in  a  gase- 
ous form  in  the  corona,  but 
as  yet  unrecognized  on  the 
earth.  Also  there  are  dark 
lines,  indicating  much  reflected 
sunlight,  possibly  coming  from 
meteoric  matter  surrounding 
the  sun.  Deslandres,  by  pho- 

Coronaof  1871  (Lord  Lindsay;  tographing  on  a  single  plate 

the  spectrum  of  the  corona  on 
opposite  sides  of  the  sun,  obtained  a  displacement  of  its  bright  line, 
showing  that  eastern  filaments  are  approaching  the  earth,  and  western 
receding  from  it ;  and  the  calculated  velocities  indicate  that  the  corona 
revolves  with  the  sun.  Independent  proof  of  the  solar  origin  of  the 
corona  is  thus  afforded. 


Periodicity  of  the  Corona  301 

Periodicity  of  the  Corona.  —  At  no  two  eclipses  of  the 
sun  is  the  corona  alike.  How  rapidly  it  varies  is  not  yet 
found  out,  but  observa- 
tions of  the  total  eclipse 
of  1893  showed  that  the 
corona  was  exactly  the 
same  in  Africa  as  when 
photographed  in  Chile 
2^  hours  earlier.  Slow 
periodic  variations  are 
known  to  take  place, 
seeming  to  follow  the 
i  i-year  cycle  of  the  spots 
on  the  sun.  At  the  time 

Of     maximum    spots,    the  Corona  of  ,  882  ^hus.er  and  Wes,=y, 

corona  is  made  up  of  an 

abundance   of   short,    bright,    and   interwoven    streamers, 
rather   fully  developed    all    around  the  sun,  as    in  these 

three  photographs  (India 
1871,  Egypt  1882,  and 
Africa  1893).  At  or  near 
the  sun-spot  minimum, 
on  the  other  hand,  the 
corona  is  unevenly  de- 
veloped :  there  are  beau- 
tiful, short,  tufted 
streamers  around  the 
solar  poles,  and  outward 
along  the  ecliptic  extend 
the  streamers,  millions 
of  miles  in  length,  as 

Corona  of  1893  vDeslandres)  . '  ,  ^. 

pictured  in  the  photo- 
graphs (next  page)  of  total  eclipses  in  the  United  States  in 
1878  and  1889.  If  a  similar  form  is  repeated  in  the  eclipse 


302 


Eclipses  of  Sun  and  Moon 


Corona  of  1878  (Harkness) 


of  1900,  the  cycle  will  be  established  ;  but  no  sufficient  expla- 
nation of  this  periodicity  of  the  corona  has  yet  been  given. 

Important  Modern 
Eclipses  of  the  Sun. — 
Not  until  the  European 
eclipse  of  1842  did  the 
true  significance  of  cir- 
cumsolar phenomena 
begin  to  be  appreciated. 
In  the  eclipses  of  1851 
and  1860  it  was  proved 
that  prominences  and 
corona  belong  to  the  sun, 
and  not  to  the  moon. 
Just  after  the  eclipse  of 
1868  (India)  was  made 
the  important  discovery  that  prominences  can  be  observed 
at  any  time  without  an  eclipse  by  means  of  the  spectro- 
scope. In  1869  (United 
States),  bright  lines  were 
found  in  the  spectrum  of 
the  corona,  one  line  in 
the  green  showing  the 
presence  of  an  element 
not  yet  known  on  the 
earth,  and  hence  called 
coronium.  In  1870 
(Spain),  the  reversing 
layer  was  discovered,  and 
in  1878  (United  States), 
a  vast  extension  of  the 

i  ,  Corona  of  1889  (Pritchett) 

coronal  streamers  about 

1 1   million  miles  both  east  and  west  of    the  sun  (shown 

above  only  in  part).     In  1882  (Egypt),  the  spectrum  of  the 


The  Next  Total  Eclipse 


303 


corona  was  first  photographed;  and  in  1889  (California), 
fine  detail  photographs  of  the  corona  were  obtained.  In 
1893  (Africa),  it  was  shown  that  the  corona  rotates  bodily 
with  the  sun;  also  in  1896  (Nova  Zembla),  and  1898 
(India),  actual  spectrum*  photographs  of  the  reversing 
layer  established  its  existence  conclusively. 

A  Total  Eclipse  near  at  Hand.  —  The  total  eclipse  of  the  sun  on 
28th  May,  1900,  occurring  in  this  part  of  the  world  and  in  the  early 
future,  a  map  of  its  path  across  the  Southern  States  is  given  below. 


Path  of  Total  Eclipse  of  28th  May,  1900,  through  the  Southern  States 

The  central  line  stretches  from  New  Orleans  to  Raleigh,  both  these 
places  being  very  near  the  middle  of  the  path.  The  average  width 
of  the  eclipse  track,  or  region  within  which  the  eclipse  will  be  total, 
is  55  miles.  Along  the  central  line  the  duration  of  total  eclipse  varies, 
from  i  m.  153.  in  Louisiana  to  i  m.  455.  in  North  Carolina.  Along 
the  lines  marked  '  Northern  and  Southern  Limits  of  Total  Eclipse,' 
the  sun  will  remain  totally  obscured  for  only  an  instant.  At  points  in- 
termediate between  the  central  line  and  either  the  northern  or  south- 
ern limits,  the  length  of  totality  will  vary  between  its  duration  on  the 
central  line  and  os.  on  the  limiting  lines  themselves.  The  total  phase 
in  this  region  will  take  place  between  half-past  seven  in  the  morning, 
at  New  Orleans,  and  ten  minutes  before  nine  at  Norfolk ;  and  nearly 
a  half  hour  of  absolute  time  will  elapse  while  the  moon's  shadow  is 


304 


Eclipses  of  Sun  and  Moon 


traveling  across  this  part  of  the  United  States.  After  leaving  Virginia, 
it  sweeps  over  the  Atlantic  Ocean,  and  southeasterly  across  Portugal, 
Spain,  and  northern  Africa. 

Important  Future  Eclipses.  —  Total  eclipses  of  the  sun 
in  the  coming  quarter  century  are  for  the  most  part  visible 
in  foreign  lands.  The  paths  of  only  two  cross  the  United 
States.  Following  are  dates  of  the  more  important  future 
eclipses,  regions  of  general  visibility,  and  approximate 
duration  of  the  total  phase :  — 


1900,  May  28 

1901,  May  18 
1905,  August  30 
1907,  January  14 
1912,  October  10 
1914,  August  21 
1916,  February  3 

1918,  June  8 

1919,  May  29 


Louisiana  to  Virginia  2  min. 

Sumatra,  Borneo,  and  Celebes  6  " 

Labrador,  Spain,  and  Egypt  4  " 

Russia  and  China  2  " 

Colombia  and  Brazil  i  " 

Norway,  Sweden,  and- Russia  2  " 

Northern  South  America  2  " 

Oregon  to  Florida  2  " 

Brazil  and  West  Africa  6  " 


Exact  times  and  circumstances  of  all  these  eclipses  are 
regularly  published  in  the  Nautical  Almanac,  issued  by  the 


Earth's  Shadow  and  Penumbra  in  Section 


English,   German,   French,   and    American    governments, 
two  or  three  years  in  advance.     No  total  eclipse  will  be 


Lunar  Eclipses  305 

visible  in  New  England  or  the  Middle  States  till  24th  Jan- 
uary, 1925,  when  the  track  of  one  will  pass  near  Portland, 
Maine.  The  great  total  eclipses  of  1955  (India),  and  1973 
(Africa)  will  exceed  7  minutes  in  duration,  the  longest  for 
a  thousand  years. 

Eclipses  of  the  Moon.  —  As  all  dark  celestial  bodies  cast 
long,  conical  shadows  in  space,  any  non-luminous  body 
passing  into  the  shadow  of  another  is  necessarily  darkened 
or  eclipsed  thereby.  When,  in  her  journey  round  our  earth, 
the  moon  comes  exactly  opposite  the  sun,  or  nearly  so,  she 


Lunar  Eclipse  of  lOjs  Digits  Lunar  Eclipse  one  Digit  short  of  Totality 

passes  through  our  shadow.  Then  a  lunar  eclipse  takes 
place.  Refer  to  illustrations  given  on  pages  290  and  291  : 
clearly,  a  lunar  eclipse  can  happen  only  when  the  moon 
is  full,  or  at  opposition.  There  is  not  an  eclipse  of  the 
moon  every  month,  because  unless  she  is  near  the  plane 
of  the  ecliptic,  that  is,  near  her  node  at  the  time,  she 
will  pass  above  or  below  the  earth's  shadow.  There  are 
partial  eclipses  of  the  moon  as  well  as  of  the  sun ;  but  in 
this  case  the  eclipse  is  partial  because  the  moon  passes 
only  through  the  edge  of  our  shadow  (lower  orbit  in  the 
illustration  opposite),  and  so  is  not  wholly  darkened.  The 
eclipse  may  be  total,  however  (upper  of  the  three  orbits), 
without  our  satellite  passing  directly  through  the  center  of 
the  earth's  shadow,  because  that  shadow,  where  the  moon 
TODD'S  ASTRON.  —  20 


306  Eclipses  of  Sun  and  Moon 

passes  through  it,  is  nearly  three  times  the  moon's  own 
diameter.  A  lunar  eclipse  is  always  visible  to  that  entire 
hemisphere  of  our  globe  turned  moonward  at  the  time. 
The  total  phase  lasts  nearly  two  hours,  and  the  whole 
eclipse  often  exceeds  three  hours  in  duration. 

The  magnitude  of  a  lunar  eclipse  is  often  expressed  by  digits,  that 
is,  the  number  of  twelfths  of  the  moon's  diameter  which  are  within  the 
earth's  umbra.  The  last  illustrations  show  different  magnitudes  of 
lunar  eclipse ;  note  the  roughness  of  the  terminator.  Also  the  same 
thing  may  be  expressed  decimally,  an  eclipse  whose  magnitude  is  i  .o 
occurring  when  the  moon  enters  the  dark  shadow  for  a  moment,  and  at 
once  begins  to  emerge. 

Diameter  of  the  Earth's  Shadow. — As  the  mean  distance  of  our 
satellite  is  239,000  miles,  the  earth's  shadow  must  extend  into  space 
beyond  the  moon  a  distance  equal  to  the  moon's  distance  subtracted 
from  the  length  of  the  shadow,  or  618,000  miles.  The  diameter  of  the 
earth's  shadow  where  the  moon  traverses  it  during  a  lunar  eclipse  may, 
therefore,  be  found  from  the  proportion 

857,000  :  7900  :  :  618,000  :  x. 

This  gives  5700  miles,  or  2|  times  the  moon's  diameter.  As  our  satel- 
lite moves  over  her  own  diameter  in  about  an  hour,  a  central  eclipse 
may  last  about  four  hours,  from  the  time  the  moon  first  begins  to  enter 
shadow  to  the  time  of  complete  emersion  from  it. 

Lunar  Ecliptic  Limit.  —  As  our  satellite  revolves  round  us  in  a  plane 
inclined  to  the  ecliptic,  it  is  evident  that  there  must  be  a  great  variety 

ECLIPSE  TOTAL 

BUT 

ECLIPSE  TOTAL  NOT  CENTRAL 

AND  CENTRAL 


Lunar  Ecliptic  Limit  West  of  Moon's  Ascending  Node 

of  conditions  under  which  eclipses  of  the  moon  take  place.  All  depends 
upon  the  distance  of  the  center  of  the  earth's  shadow  from  the  node  of 
the  moon's  orbit  at  the  time  of  full  moon.  The  illustration  helps  to 
make  this  point  plain.  It  shows  a  range  in  magnitude  of  eclipse,  frorA 
the  total  and  central  obscuration  (on  the  left),  to  the  circumstances 
which  just  fail  to  produce  an  eclipse  (on  the  right).  The  arc  of  the 


Moon    Visible  although  Eclipsed  307 


ecliptic,  about  12°  long,  included  between  these  two  extremes,  is  called 
the  lunar  ecliptic  limit.  It  varies  in  length  with  our  distance  from  the 
sun ;  evidently  the  farther  we  are  from  the  sun,  the  larger  will  be  the 
diameter  of  the  earth's  shadow.  Also  the  lunar  ecliptic  limit  varies 
with  the  moon's  distance  from  us ;  because  the  nearer  she  is  to  us,  the 
greater  the  breadth  of  our  shadow  which  she  must  traverse.  Inside  of 
this  limit,  the  moon  may  come  to  the  full  at  any  distance  whatever  from 
the  nodes.  Clearly  there  is  a  limit  of  equal  length  to  the  east  of  the 
node  also ;  and  the  entire  range  along  the  ecliptic  within  which  a  lunar 
eclipse  is  possible  is  nearly  25°,  As  the  sun  (and  consequently  the 
earth's  shadow)  consumes  about  26  days  in  traversing  this  arc,  there  is 
an  interval  of  nearly  a  month  at  each  node,  or  twice  a  year,  during 
which  a  lunar  eclipse  is  possible. 

The  Moon  still  Visible  although  Eclipsed.  —  Usually  the 
moon,  although  in  the  middle  of  the  earth's  shadow  where 
she  can  receive  no  direct  light  from  the  sun,  is  neverthe- 
less visible  because  of  a  faint,  reddish  brown  illumination. 
Probably  this  is  due  to  light  refracted  through  the  earth's 
atmosphere  all  around  the  sunrise  and  sunset  line.  At- 
mosphere absorbs  nearly  all  the  bluish 
rays,  allowing  the  reddish  ones  to  pass 
quite  freely. 

Naturally,  if  this  belt  of  atmosphere  were  per- 
fectly clear,  the  darkened  portion  of  the  moon 
might  be  plainly  visible  as  in  the  picture  of 
the  eclipse  of  1895  (page  308),  while  if  it  were 
nearly  filled  with  cloud,  very  little  light  could 
pass  through  and  fall  upon  the  moon ;  so  that 
when  she  had  reached  the  middle  of  the 
shadow,  she  would  totally  disappear.  Accord- 
ingly there  are  all  variations  of  the  moon's 
visibility  when  totally  eclipsed;  in  1848,  so 

bright  was  it  that  some  doubted  whether  there  Total  Lunar  Eclipse,  3dSep- 
really  was  an  eclipse  ;  while  in  1 884  the  coppery 
disk  of  the  moon  disappeared  so  completely 
that  she  could  scarcely  be  seen  with  the  telescope.  In  September  1895 
the  moon,  even  when  near  the  middle  of  our  shadow,  gave  light  enough 
to  enable  Barnard  to  obtain  this  photograph  of  the  total  eclipse,  by 
making  a  long  exposure,  which  accounts  for  the  stars  being  trails 
instead  of  mere  dots ;  for  the  clockwork  was  made  to  follow  the  mov- 


tember,      1 895      (photo- 
graphed  by  Barnard) 


308 


Eclipses  of  Sun  and  Moon 


ing  moon.  Total  lunar  eclipses  are  of  use  to  the  astronomer  in  meas- 
uring the  variation  of  heat  radiated  at  different  phases  of  the  eclipse. 
Also  the  occultations  of  faint  stars  can  be  accurately  observed,  as  the 
moon's  disk  passes  over  them ;  and  by  combining  a  large  number  of 
these  observations  at  widely  different  parts  of  the  earth,  the  moon's  size 
and  distance  can  be  more  precisely  ascertained.  Only  one  total 
eclipse  will  be  visible  in  America  during  the  remainder  of  the  pres- 
ent century.  It  occurs  27th  December,  1898.  Total  eclipse  begins  at 
5.49  P.M.,  the  middle  of  the  eclipse  is  at  6.34,  and  the  end  of  total 
eclipse  takes  place  at  7.18  P.M.,  Eastern  Standard  time.  So  that  it 
may  be  well  observed  in  the  eastern  part  of  the  United  States. 


Lunar  Eclipse  just  before  Totality,  observed  at  Amherst  College,   10th  March,   1895 

Relative  Frequency  of  Solar  and  Lunar  Eclipses.  —  Draw  lines  tangent 
to  sun  and  earth,  as  in  next  figure.  An  eclipse  of  the  moon  takes  place 
whenever  our  satellite,  near  M' ,  passes  into  the  dark  shadow  cone.  On 
the  other  hand,  when  near  J/,  a  solar  eclipse  happens  if  the  moon 
touches  any  part  of  the  earth's  shadow  cone  extended  sunward  from  E. 
As  the  breadth  of  this  shadow  cone  is  greater  at  M  than  at  J/',  ob- 
viously the  moon  must  infringe  upon  it  more  often  at  M ;  that  is, 
eclipses  of  the  sun  are  more  frequent  than  eclipses  of  the  moon.  Cal- 
culation shows  that  the  relative  frequency  is  about  as  4  to  3.  This 


Eclipse  Seasons  309 

means  simply  with  reference  to  the  earth  as  a  whole.     If,  however,  we 

compare  the  relative  frequency  of  solar  and  lunar  eclipses  visible  in  a 

given  country,  it  will  be  found  that  lunar  eclipses  are  much  more  often 

seen  than  solar  ones.     This  is 

because    some    phase    of  every 

lunar    eclipse    is    visible    from 

more   than  half  of  our    globe, 

while  a  solar  eclipse  can  be  seen 

from  only  that  limited  part  of  " ^ore  Sokr  than  Lunar  Edipses 

the    earth's    surface    which    is 

traversed   by  the  moon's  umbra  and   penumbra.     If  we  consider  the 

narrow  trail  of  the  umbra  alone,  a  total  solar  eclipse  will  be  visible  from 

a  given  place  only  once  on  the  average  in  350  years. 

Eclipse  Seasons.  —  It  has  been  shown  that  eclipses  of  sun  and  moon 
can  happen  only  when  the  sun  is  near  the  moon's  node.  Were  these 
points  stationary,  it  is  clear  that  eclipses  would  always  take  place  near 
the  same  time  every  year.  But  the  westward  motion  of  the  nodes  is 
such  that  they  travel  completely  round  the  ecliptic  in  18^  years.  The 
sun,  then,  does  not  have  to  go  all  the  way  round  the  sky  in  order  to 
return  to  a  node ;  and  the  interval  elapsing  between  two  consecutive 
passages  of  the  same  node  is  only  346*  days.  This  is  called  the  eclipse 
year.  On  the  average,  then,  eclipses  happen  nearly  three  weeks  earlier 
in  each  calendar  year.  The  midyear  eclipses  of  1898  take  place  in  July, 
of  1899  in  June,  and  of  1900  in  May.  Each  passage  of  a  node  marks 
the  middle  of  a  period  during  which  the  sun  is  traveling  over  an  arc 
equal  to  double  the  ecliptic  limit.  No  eclipse  can  happen  except  at 
these  times.  They  are,  therefore,  called  eclipse  seasons.  As  the  solar 
ecliptic  limit  exceeds  the  lunar,  so  the  season  for  eclipses  of  the  sun 
exceeds  that  for  lunar  eclipses :  the  average  duration  of  the  former  is 
37  days,  and  of  the  latter  23. 

Recurrence  and  the  Saros.  —  Ever  since  the  remote  age 
of  the  Chaldeans,  B.C.  700,  has  been  known  a  period  called 
the  saros,  by  which  the  return  of  eclipses  can  be  roughly 
predicted.  The  length  of  the  saros  is  6585^  days,  or  18 
years  11^  days.  At  the  end  of  this  period,  the  centers  of 
sun  and  moon  return  very  nearly  to  their  relative  positions 
at  the  beginning  of  the  cycle ;  also  certain  technical  con- 
ditions relating  to  the  moon's  orbit  and  essential  to  the 
accuracy  of  the  saros  are  fulfilled.  Solar  and  lunar  eclipses 
are  alike  predictable  by  it. 


310  Eclipses  of  Sun  and  Moon 

A  total  eclipse  of  the  sun  occurred  in  Egypt,  I7th  May,  1882  ;  and 
reckoning  forward  from  that  date  by  means  of  the  saros,  we  can  pre- 
dict the  eclipses  of  28th  May,  1900,  and  8th  June,  1918.  But  only  in  a 
general  way ;  if  the  precise  circumstances  of  the  eclipse  are  required, 
and  the  places  where  it  will  be  visible,  a  computation  must  be  made  from 
the  Ephemeris,  or  Nautical  Almanac.  Mark  the  effect  of  the  one  third 
day  in  the  saros:  the  eclipse  at  each  recurrence  falls  visible  about  120° 
of  longitude  farther  west;  in  1882  visible  in  Egypt,  in  1900  on  the 
Atlantic  Ocean,  in  1918  on  the  Pacific  Ocean.  A  period  of  54  years 
I  month  i  day,  or  three  times  the  length  of  the  saros,  will  therefore 
bring  a  return  of  an  eclipse  in  very  nearly  the  same  longitude,  but  its 
track  will  always  be  displaced  several  hundred  miles  in  latitude.  For 
example,  the  total  eclipse  of  8th  July,  1842,  was  observed  in  central 
Europe  ;  but  its  return,  9th  August,  1896,  fell  visible  in  Norway.  About 
70  eclipses  usually  take  place  during  a  saros,  of  which  about  40  are 
eclipses  of  the  sun,  and  30,  of  the  moon. 

Life  History  of  an  Eclipse.  —  As  to  eclipses  in  their  relation  to  the 
saros.  every  eclipse  may  be  said  to  have  a  life  history.  Whatever  its 
present  character,  whether  partial,  total,  or  annular,  it  has  not  always 
been  so  in  the  past,  nor  will  its  character  continue  unchanged  in  the 
indefinite  future.  New  and  very  small  partial  eclipses  of  the  sun  are 
born  at  the  rate  of  about  four  every  century ;  they  grow  to  maturity  as 
total  and  annular  eclipses,  and  then  decline  down  their  life  scale  as 
merely  partial  obscurations,  becoming  smaller  and  smaller  until  even 
the  moon's  penumbra  fails  to  touch  the  earth,  and  the  eclipse  completely 
disappears.  For  a  lunar  eclipse,  this  long  cycle  embraces  nearly  900 
years,  that  is,  the  number  of  returns  according  to  the  saros  is  almost 
50 ;  but  solar  eclipses,  for  which  the  ecliptic  limit  is  larger,  will  return 
nearly  70  times,  and  last  through  a  cycle  of  almost  1200  years. 

Occultations  of  Stars  and  Planets  by  the  Moon.  —  Closely  allied  to 
eclipses  are  the  phenomena  called  occultations.  When  the  moon  comes 
in  between  the  earth  and  a  star  or  planet,  our  satellite  is  said  to  occult 
it.  There  are  but  two  phases,  the  disappearance  and  the  reappearance  ; 
and  in  the  case  of  stars,  these  phases  take  place  with  startling  suddenness. 
Disappearances  between  new  and  full,  and  reappearances  between  full 
and  new,  are  best  to  observe,  because  they  take  place  at  the  dark  edge 
or  limb  of  the  moon.  When  the  crescent  is  slender,  a  very  small  tele- 
scope is  sufficient  to  show  these  interesting  phenomena  for  the  brighter 
stars  and  planets.  Occultations  of  the  Pleiades  are  most  interesting  and 
important.  Many  hundreds  of  occultations  of  stars  are  predicted  in  the 
Nautical  Almanac  each  year.  Occultations  of  the  major  planets  are  very 
rare,  and  none  can  be  well  seen  in  the  United  States  during  the  remain- 
der of  the  I9th  century. 


CHAPTER   XIII 

THE   PLANETS 

TETHERED  by  an  overmastering  attraction  to  the 
central  and  massive  orb  of  the  solar  system  are  a 
multitude   of   bodies    classified   as   planets.       Next 
beyond  the  moon,  they  are  nearest  to  us  of  all  the  heavenly 
spheres,  and  telescopes   have   on   that   account   afforded 
astronomers  much  knowledge  concerning  them.     But  be- 
fore presenting  this  we  first  consider  their  motions,  and  the 
aspects  and  phases  which  they  from  time  to  time  exhibit. 

Motions  —  Classification  —  Aspects  —  Phases 

Apparent  Motions  of  the  Planets.  —  Watch  the  sky  from 
night  to  night.  Nearly  all  the  bright  stars,  likewise  the 
faint  ones,  appear  to  be  fixed  on  the  revolving  celestial 
sphere ;  that  is,  they  do  not  change  their  positions  with 
reference  to  each  other.  But  at  nearly  all  times,  one  or 
two  bright  objects  are  visible  which  evidently  do  not  belong 
to  the  great  system  of  the  stars  considered  as  a  whole; 
these  shift  their  positions  slowly  from  week  to  week,  with 
reference  to  the  fixed  stars  adjacent  to  them.  The  most 
ancient  astronomers  detected  these  apparent  motions,  and 
gave  to  such  bodies  the  general  name  of  planets ;  that  is, 
wanderers.  Their  movements  among  the  stars  appear  to 
be  very  irregular  —  sometimes  advancing  toward  the  east, 
then  slowing  down  and  finally  remaining  nearly  stationary 
for  different  lengths  of  time,  and  again  retrograding,  that 

3" 


312 


The  Planets 


is,  moving  toward  the  west.  But  their  advance  motion 
always  exceeds  their  motion  westward,  so  that  all,  in  greater 
or  less  intervals,  journey  completely  round  the  heavens. 
None  of  the  brighter  ones  are  ever  found  outside  of  the 
zodiac ;  in  fact,  Mercury,  which  travels  nearest  to  the  edge 
of  this  belt,  is  always  about  two  moon  breadths  within  it. 
A  study  of  the  apparent  motions  of  all  the  planets  reveals 
a  great  variety  of  curves.  If  the  motions  of  the  planets 
could  be  watched  from  the  sun,  there  would  be  no  such 
complication  of  figures ;  for  they  exist  only  because  we 
observe  from  the  earth,  itself  one  of  the  planets,  and  con- 
tinually in  motion  as  the  other  sun-bound  bodies  are. 
Planets*  Motions  explained  by  the  Epicycle.  —  The  irregu- 
lar motions  of  the 
planets  among  the 
stars  were  ingen- 
iously explained 
by  the  ancient 
astronomers  from 
the  time  of  Hip- 
parchus(B.c.  130) 
onward,  by  means 
of  the  epicycle. 
A  point  which 
moves  uniformly 
round  the  circum- 
ference of  a  small 
circle  whose  cen- 

A  Planet's  Motion  in  the  Epicycle  £gr      travels       Uni- 

formly  round   the    periphery   of   a   large    one,  is  said  to 
describe  an  epicycle. 

The  figure  should  make  this  plain:  the  center,  c,  of  the  small  circle, 
called  the  epicycle,  moves  round  the  center  t  of  the  large  circle,  called 
the  deferent ;  and  at  the  end  of  each  24th  part  of  a  revolution,  it  occu- 


Their  Naked-eye  Appearance  313 

pies  successively  the  points  i,  2,  3,  4,  5,  and  so  on.  But  while  c  is  mov- 
ing to  i,  the  point  a  is  traversing  an  arc  of  the  deferent  equal  to  albr 
By  combination  of  the  two  motions,  therefore,  the  point  a  will  traverse 
the  heavy  curve,  reaching  the  points  indicated  by  bv  by  £3,  bv  b5,  when 
c  arrives  at  corresponding  points  1,2,3,4,5.  In  passing  from  b%  to 
AI,  the  planet  will  turn  backward,  or  seem  to  describe  its  retrograde 
arc  among  the  stars.  By  combining  different  rates  of  motion  with  cir- 
cles of  different  sizes,  it  was  found  that  all  the  apparent  movements  of 
the  planets  could  be  almost  perfectly  explained.  This  false  system, 
advanced  by  Ptolemy  (A.D.  140)  in  his  great  work  called  the  Almagest, 
was  in  vogue  until  overthrown  by  Copernicus  on  the  publication  of  his 
great  work  De  Revolutionibus  Corporum  Coelestium  in  1543. 

Naked-eye  Appearance  of  the  Planets.  —  Mercury  can 
often  be  seen  in  all  latitudes  of  the  United  States  by. 
looking  just  above  the  eastern  horizon  before  sunrise 
(in  August,  September,  or  October),  or  just  above  the 
western  horizon  after  sunset  (in  February,  March,  or 
April).  In  these  months  the  ecliptic  stands  at  a  very 
large  angle  with  the  horizon,  and  Mercury  will  appear  as 
a  rather  bright  star  in  the  twilight  sky,  always  twinkling 
violently.  Venus,  excepting  sun  and  moon  the  brightest 
object  in  the  sky,  is  known  to  everybody.  She  is  always  so 
much  brighter  than  any  of  the  other  planets  that  she  cannot 
be  mistaken  —  either  easterly  in  the  early  mornings  or 
westerly  after  sunset,  according  to  her  orbital  position  rela- 
tively to  the  earth.  Usually,  when  passing  near  the  sun, 
Venus  cannot  be  seen  because  the  sun  overpowers  her 
rays.  During  periods  of  greatest  brilliancy,  however, 
Venus  is  not  difficult  to  see  with  the  naked  eye  when  near 
the  meridian  in  a  clear  blue  sky.  Mars,  when  visible,  is 
always  distinguishable  among  the  stars  by  a  brownish 
red  color.  Distance  from  both  earth  and  sun  varies  so 
greatly  that  he  is  sometimes  very  faint,  and  again  when 
nearest,  exceedingly  bright.  Jupiter  comes  next  to  Venus 
in  order  of  planetary  brightness.  Though  much  less  bright 
than  Venus,  he  is  still  brighter  than  any  fixed  star.  Saturn 


3 14  The  Planets 

is  difficult  to  distinguish  from  a  star,  because  he  shines 
with  about  the  order  of  brightness  of  a  first  magnitude 
star.  His  light  has  a  yellowish  tinge,  and  by  looking 
closely,  absence  of  twinkling  will  be  noticed.  Unless  very 
near  the  horizon,  none  of  the  planets  except  Mercury  ever 
twinkle ;  and  this  simple  fact  helps  to  distinguish  them 
from  fixed  stars  near  them.  Uranus,  just  on  the  limit  of 
visibility  without  the  telescope  may  be  seen  during  spring 
and  summer  months,  if  one  has  a  keen  eye  and  knows 
just  where  to  look.  Also  Vesta,  one  of  the  small  planets, 
may  at  favorable  times  be  seen  without  a  telescope.  Nep- 
tune is  never  visible  without  optical  aid. 

Convenient  Classifications  of  the  Planets.  —  Neither  appar- 
ent motion,  nor  naked-eye  appearance,  however,  affords 
any  basis  for  classification  of  the  planets.  But  distance 
from  the  sun  and  size  do.  In  order  of  distance,  succession 
of  the  eight  principal  planets  with  their  symbols  is  as 
follows,  proceeding  from  the  sun  outward:  — 

$  Mercury,  9  Venus,  0  Earth,  $  Mars,  ^  Jupiter, 
b  Saturn,  $  Uranus,  W  Neptune.  Of  these,  Mercury  and 
Venus,  whose  orbits  are  within  the  earth's,  are  classified  as 
inferior  planets,  and  the  other  five  from  Mars  to  Neptune, 
as  superior  planets.  In  the  same  category  would  be  in- 
cluded the  ring  of  asteroids,  or  small  planets,  between  Mars 
and  Jupiter.  The  real  motions  of  the  planets  round  the 
sun  are  counter-clockwise,  or  from  west  toward  east. 

Also  the  planets  are  often  conveniently  classified  in 
three  distinct  groups  :  — 

(I)  The  inner  or  terrestrial  planets,   Mercury,  Venus, 
Earth,  Mars  ;  also  the  unverified  intramercurian  bodies. 

(II)  The  asteroids,  or  small  planets,  sometimes  called 
planetoids,  or  minor  planets. 

(III)  The    outer    or    major    planets,    Jupiter,    Saturn, 
Uranus,  Neptune. 


Configurations  of  Inferior  Planets         315 

In  this  classification  the  zone  of  asteroids  forms  a  definite  line  of 
demarcation ;  but  the  basis  is  chiefly  one  of  size,  for  all  the  terrestrial 
planets  are  very  much  smaller  than  the  outer  or  major  planets.  Here 
may  be  included  also  the  zodiacal  light,  and  the  gegenschein*  both  faint, 
luminous  areas  of  the  nightly  sky.  Probably  their  light  is  mere  sun- 
light reflected  from  thin  clouds  of  meteoric  matter  entitled  to  considera- 
tion as  planetary  bodies,  because,  like  the  planets,  each  particle  must 
pursue  its  independent  orbit  round  the  sun.  All  the  planetary  bodies 
of  whatever  size,  together  with  their  satellites,  the  sun  itself,  and  mul- 
titudes of  comets  and  meteors,  are  often  called  the  solar  system. 

Configurations  of  Inferior  Planets.  —  In  consequence  of 
their  motions  round  the  central  orb,  Mercury  and  Venus 


Aspects  of  Inferior  and  Superior  Planets 

regularly  come  into  line  with  earth  and  sun,  as  illustrated 
in  above  diagram.  If  the  planet  is  between  us  and  the 
sun,  this  configuration  is  called  inferior  conjunction  ;  supe- 
rior conjunction,  if  the  planet  is  beyond  that  luminary. 
At  inferior  conjunction,  distance  from  earth  is  the  least 
possible;  at  superior  conjunction,  the  greatest  possible. 
On  either  side  of  inferior  conjunction  the  inferior  planets 
attain  greatest  brilliancy ;  with  Mercury  this  occurs  about 
three  weeks,  and  with  Venus  about  five  weeks,  preceding 
and  following  inferior  conjunction.  For  many  days  near 


The  Planets 


this  time,  Venus  is  visible  in  the  clear  blue  even  at  mid- 
day ;  but  in  a  dark  sky  her  radiance  is  almost  dazzling, 
and  with  every  new  recurrence  she  deceives  the  uneducated 
afresh. 

Near  her  western  elongation,  in  1887-88,  many  thought  she  was  the 
'Star  of  Bethlehem  1 ;  and  for  weeks  in  the  winter  and  spring  of  1897, 
when  Venus  shone  high  above  the  horizon,  multitudes  in  New  England 
gave  credence  to  a  newspaper  story  that  the  brilliant  luminary  which 
glorified  the  western  sky  was  an  electric  light  attached  to  a  balloon 
sent  up  from  Syracuse,  and  hauled  down  slowly  every  night  about 
9  P.M.  Venus  will  again  attain  her  greatest  brilliancy  on 

27th  October,  1898,  elongation  east,  also  on 
5th  January,  1899,  elongation  west; 

but  what  stories  may  then  be  set  going  is  idle  to  surmise. 

Greatest  Elongation  of  Inferior  Planets.  —  An  inferior 
planet  is  at  greatest  elongation  when  its  angular  distance 

from  the  sun,  as  seen 
from  the  earth,  is  as  great 
as  possible.  The  follow- 
ing illustrations  help  to 
make  these  points  clear. 
The  earth  is  at  the  eye 
of  the  observer,  and  a 
thin  disk  about  18  inches 
in  diameter,  and  held 
about  one  foot  from  the 
eye,  represents  the  plane 
of  the  orbits  of  the  in- 
ferior planets.  They 
travel  round  with  the 
arrows,  passing  superior 
conjunction  when  farthest  away  from  the  eye,  and  there- 
fore of  their  smallest  apparent  size.  Coming  round  to 
greatest  elongation,  they  are  nearer  and  larger,  and  their 
phase  is  that  of  the  quarter  moon.  The  angle  between 


Inferior  Planets  at  Greatest  Elongation  East 
(after  Sunset  in  Spring) 


Configurations  of  Superior  Plane  Is        317 


Venus  and  the  sun  is  then  47°.  Mercury  at  a  like  phase 
may  be  as  much  as  28°  distant  ;  but  his  orbit  is  so  eccen- 
tric that  if  he  is  near  perihelion  at  the  same  time,  he 
may  be  only  18°  from  the  sun. 

Passing  on  to  inferior  conjunction,  the  phase  is  a  continually 
diminishing  crescent,  of  a  gradually  increasing  diameter,  as  shown. 
The  opposite  figure  represents 
the  apparent  position  of  the  or- 
bits (relative  to  horizon)  when 
the  greatest  eastern  elonga- 
tions occur  in  our  springtime. 
The  observer  is  looking  west 
at  sunset,  and  the  planets  at 
elongation  shine  far  above  the 
horizon  in  bright  twilight,  and 
are  best  and  most  conveniently 
seen.  When  greatest  elonga- 
tions west  of  the  sun  occur, 
one  must  look  eastward  for 
them,  before  sunrise,  as  in  the 
adjacent  illustration  (autumn 
inclination  to  east  horizon). 
The  ancients  early  knew  that 
Venus  in  these  two  relations 
was  one  and  the  same  planet  ; 

but  they  preserved  the  poetic  distinction  of  a  double  name,  —  Phos- 
phorus for  the  morning  star,  and  Hesperus  for  the  evening. 

Configurations  of  Superior  Planets.  —  By  virtue  of  the 
position  of  superior  planets  outside  our  orbit,  they  may 
recede  as  far  as  180°  from  the  sun.  Being  then  on  the 
opposite  side  of  the  celestial  sphere,  they  are  said  to  be  in 
opposition  (page  315).  When  in  the  same  part  of  the 
zodiac  with  the  sun,  they  are  in  conjunction.  Halfway 
between  these  two  configurations  a  superior  planet  is  in 
quadrature;  that  is,  an  elongation  of  90°  from  the  sun. 
Opposition,  conjunction,  and  quadrature  usually  refer  to 
the  ecliptic,  and  the  angles  of  separation  are  arcs  of 
celestial  longitude,  nearly.  Sometimes,  however,  it  is 


Inferior  Planets  at  Greatest  E.ongation  West 
(before  Sunrise  in  Autumn) 


OF  THK 

UNIVERSITY 


318  The  Planets 

necessary  to  use  conjunction  in  right  ascension..  Inferior 
planets  never  come  in  opposition  or  even  quadrature,  be- 
cause their  greatest  elongations  are  much  less  than  90°. 

The  Phases  of  the  Planets.  —  Some  of  the  planets,  as 
observed  with  the  telescope,  are  seen  to  pass  through  all 
the  phases  of  the  moon.  Others  are  seen  at  times  to 
resemble  certain  lunar  phases ;  while  still  others  have  no 


Phases  and  Apparent  Size  of  the  Planet  Mercury 

phase  whatever.  To  the  first  class  belong  the  inferior 
planets,  Mercury  and  Venus.  On  approaching  inferior 
conjunction,  their  crescent  becomes  more  and  more 
slender,  like  that  of  the  very  old  moon  when  coming  to 
new;  while  from  inferior  conjunction  to  superior  conjunc- 
tion, they  pass  through  all  the  lunar  phases  from  new  to 
full.  As  in  the  case  of  the  moon,  the  horns  of  the  cres- 
cent are  always  turned  from  the  sun  (toward  it,  as  seen  in 
the  inverting  telescope).  When  near  their  greatest  elon- 
gation, the  phase  of  these  planets  is  that  of  the  moon  at 
quarter.  One  of  Galileo's  first  discoveries  with  the  first 
astronomical  telescope,  in  1610,  was  the  phase  of  Venus. 
None  of  the  superior  planets  can  pass  through  all  the 
phases  of  the  moon,  because  they  never  can  come  be- 
tween us  and  the  sun. 

The  degree  of  phase  which  they  do  experience,  however,  is  less  in 
proportion  as  their  distance  beyond  us  is  greater.  Mars,  then,  has  the 
greatest  phase.  At  quadrature  the  planet  is  gibbous,  about  like  the  moon 
three  days  from  full.  Mars  appears  at  maximum  phase  in  plate  vi, 
page  360.  But  at  opposition,  his  disk,  like  that  of  all  other  planets, 
appears  full.  Some  of  the  small  planets,  too,  give  evidence  of  an 
appreciable  phase :  not  that  it  can  be  seen  directly,  for  their  disks  are 


Retrogressive  Motion  319 

too  small,  but  by  variation  in  the  amount  of  their  light  from  quadra- 
ture to  opposition,  as  Parkhurst  has  determined.  Jupiter  at  quadrature 
has  a  slight,  though  almost  inappreciable,  phase.  Other  exterior 
planets  —  Saturn,  Uranus,  and  Neptune  —  have  practically  none. 

Loop  of  a  Superior  Planet's  Apparent  Path  Explained.  —  Refer  to  the 
figure.  The  largest  ellipse,  ABC'D,  is  the  ecliptic.  Intermediate  ellipse 
is  orbit  of  an  exterior  planet ;  and  smallest  ellipse  is  the  path  of  earth 


D 
To  explain  Formation  of  Loop  in  Exterior  Planet's  Path 

itself.  A  planet  when  advancing  always  moves  in  direction  GH.  The 
sun  is  at  S.  When  earth  is  successively  at  points  marked  i,  2,  3,  4,  5, 
6,  7  on  its  orbit,  the  outer  planet  is  at  the  points  marked  i,  2,  3, 4,  5, 6,  7 
on  the  middle  ellipse.  So  that  the  planet  is  seen  projected  upon  the 
sky  in  the  directions  of  the  several  straight  lines.  These  intersect 
the  zone  F,  G,  //,  /,  of  the  celestial  sphere  in  the  points  also  marked 
upon  it  i,  2,  3,  4,  5,  6,  7,  and  among  the  stars  of  the  zodiac.  Fol- 
lowing them  in  order  of  number,  it  is  evident  that  the  planet  ad- 
vances from  i  to  3,  retrogrades  from  3  to  5,  and  advances  again 
from  5  to  7.  Also  its  backward  motion  is  most  rapid  from  3  to  4, 
when  the  planet  is  near  opposition,  and  its  distance  from  earth  is  the 
least  possible.  In  general,  the  nearer  the  planet  to  earth,  the  more 
extensive  its  loop. 

A  Planet  when  Nearest  Retrogrades.  —  First  consider  the 
inferior  planets  of  which  Venus  may  be  taken  as  the  type. 
Fixed  stars  are  everywhere  round  the  outer  ring,  represent- 
ing the  zodiac  (page  320).  Within  are  two  large  arrows  fly- 
ing in  the  counter-clockwise  direction  in  which  the  planets 
really  move  round  the  sun.  Earth's  orbit  is  the  outer  cir- 
cle in  the  left-hand  figure,  and  the  dotted  circle  within  is 
the  orbit  of  Venus.  As  Venus  moves  more  swiftly  than 


320 


The  Planets 


the  earth  does,  evidently  the  latter  may  be  regarded  as 
stationary,  and  Venus  as  moving  past  it  at  the  upper  part 
of  the  orbit,  where  inferior  conjunction  takes  place.  But 
Venus  in  this  position  appears  to  be  among  the  stars  far 
beyond  the  sun,  consequently  her  real  motion  forward  seems 
to  be  motion  backward  among  the  stars,  as  indicated  by 


v- 


Inferior  Planets  retrograde  at  Inferior 
Conjunction 


Superior  Planets  retrograde  at 
Opposition 


All  Planets  retrograde  when  nearest  to,  and  advance  when  farthest  from,  the  Earth 

the  right-hand  arrow  at  the  bottom.  Next,  consider  the 
exterior  planet,  of  which  Mars  may  be  taken  as  the  type. 
In  the  right-hand  figure,  inner  circle  is  orbit  of  earth,  and 
outer,  orbit  of  Mars  ;  and  as  earth  moves  more  swiftly  than 
Mars,  earth  may  be  regarded  as  the  moving  body  and  Mars 
as  stationary.  In  the  upper  part  of  the  figure  occurs  oppo- 
sition, and  earth  overtakes  Mars  and  moves  on  past  him. 
But  Mars  is  seen  among  the  stars  above  and  beyond  it,  and 
evidently  his  apparent  motion  is  westerly,  or  retrograde, 
in  the  direction  of  the  small  arrow  at  the  top  of  the  figure. 
Thus  is  reached  the  conclusion  that  the  apparent  motion 
of  all  the  planets,  whether  inferior  or  superior,  is  ahvays 
retrograde  when  they  are  nearest  the  earth. 

A  Planet  when  Farthest  Advances.  —  Return  to  the  in- 


Orbits  of  Inner  Planets  321 

ferior  planet  Venus,  and  the  left-hand  figure ;  when 
farthest  she  is  in  the  lower  part  of  her  orbit,  and  her 
apparent  position  is  among  the  stars  still  farther  below, 
west  or  to  the  left  of  the  sun.  Advance  or  eastward  mo- 
tion in  orbit,  then,  appears  as  advance  motion  forward 
among  the  stars.  Seemingly,  Venus  is  moving  toward  the 
sun,  and  will  soon  overtake  and  pass  behind  him.  Now  the 
exterior  planet  again.  Assuming  Mars  to  remain  station- 
ary in  the  position  of  the  black  dot  in  lower  part  of  orbit, 
earth  (in  upper  part  of  orbit,  where  distance  between  the 
two  is  nearly  as  great  as  possible)  moves  eastward  in  the 
direction  of  the  arrow  through  it.  As  a  consequence  of 
this  motion,  then,  Mars  seems  to  travel  forward  on  the 
opposite  or  lower  side  of  the  celestial  sphere  (in  the  direc- 
tion of  a  very  minute  arrow  near  the  bottom  of  the  figure). 
Thus  is  reached  this  general  conclusion :  The  apparent 
motion  of  all  the  planets,  whether  inferior  or  superior,  is 
always  retrograde  when  they  are  nearest  the  earth,  and 
advance  or  eastward  when  farthest  from  it. 

Orbits  —  Elements  —  Periods  —  Laws  of  Motion 

The  Four  Inner  or  Terrestrial  Planets.  —  On  next  page 
are  charted  the  orbits  of  the  four  inner  planets,  Mercury, 
Venus,  earth,  and  Mars.  Observe  that  while  Venus  and 
the  earth  move  in  paths  nearly  circular,  with  the  sun  very 
near  their  center,  orbits  of  Mercury  and  Mars  are  both 
eccentrically  placed.  So  nearly  circular  are  the  orbits  of 
all  planets  that,  in  diagrams  of  this  character,  they  are 
indicated  accurately  enough  by  perfect  circles.  Orbits 
having  a  considerable  degree  of  eccentricity  are  best  repre- 
sented by  placing  the  sun  a  little  at  one  side  of  their 
center. 

The  double  circle  outside  the  planetary  orbits  represents  the  ecliptic, 
graduated  from  o°  eastward,  or  counter-clockwise,  around  to  360°  of 
TODD'S  ASTRON.  —  21 


322 


The  Planets 


longitude,  according  to  the  signs  of  the  zodiac,  as  indicated  ;  the  vernal 
equinox,  or  the  first  point  of  the  sign  Aries  corresponding  to  o°. 
Small  black  dots  on  each  orbit  represent  positions  of  the  planets  at 
intervals  of  ten  days,  zero  for  each  planet  being  at  longitude  180°.  All 
the  planets  travel  round  the  sun  eastward,  or  counter-clockwise,  as 


SCALE  OF  MILLIONS  OF  MILES 

Orbits  and  Heliocentric  Movements  of  the  Four  Terrestrial  Planets 

indicated  by  arrows.  In  order  to  find  the  distance  of  any  planet  from 
earth,  or  from  any  other  at  any  time,  first  find  the  position  of  the  two 
planets  in  their  respective  orbits  by  counting  forward  from  the  dates 
given  for  each  planet  on  the  left-hand  side  of  the  chart,  at  longitude 
180°,  Then  with  a  pair  of  dividers  the  distance  of  the  planets  may  be 
found  from  the  scale  of  millions  of  miles  underneath. 

The  Four  Outer  and  Major  Planets.  —  Opposite  is  a  chart  of  the  orbits 
of  the  four  outer  planets,  Jupiter,  Saturn,  Uranus,  and  Neptune.     Ob- 


True  Form  of  Planetary  Orbits  323 

serve  that  these  orbits  are  all  sensibly  circular  and  concentric,  except 
that  of  Uranus,  the  center  of  which  is  slightly  displaced  from  the  sun. 
The  double  outer  circle  represents  the  ecliptic,  the  same  as  in  the 
diagram  on  the  opposite  page.  The  small  black  dots  on  the  orbits  of 
Jupiter  and  Saturn  represent  the  positions  of  these  planets  at  intervals 


2000 
SCALE  OF  MILLIONS  OF  MILES 

Orbits  and  Heliocentric  Movements  of  the  Four  Greater  Planets 

a  year  in  length ;  and  similarly,  the  positions  of  Uranus  and  Neptune 
are  indicated  at  zo-year  intervals;  the  zero  in  every  case  being  coinci- 
dent with  longitude  i8o°~  The  distance  of  these  planets  from  each 
other,  or  from  the  earth  at  any  time,  may  be  found  in  the  same  way  as 
described  on  the  opposite  page  for  the  inner  planets. 

True  Form  of  the  Planetary  Orbits.  —  Were  it  possible 
to  transport  our  observatory  and  telescope  from  earth  to 


324  The  Planets 

each  of  the  planets  in  turn,  and  then  repeat  the  meas- 
ures of  the  sun's  diameter  with  great  refinement,  just  as 
we  did  from  the  earth  (page  136),  we  should  reach  a  result 
precisely  similar  in  every  case.  So  the  conclusion  is,  that 
the  orbits  of  all  the  planets  are  ellipses,  so  situated  in 


Planetary  Orbits  having  Greater  Inclinations  to  the  Ecliptic 

sr.  ace  that  the  sun  occupies  one  of  the  foci  of  each  ellipse. 
None  of  them  would  lie  in  the  same  plane  that  the  earth 
does,  but  each  planet  would  have  an  ecliptic  of  its  own,  in 
the  plane  of  which  its  orbit  would  be  situated. 

Inclination  and  Line  of  Nodes. — The  orbits  of  all  the 
great  planets,  except  Mercury,  Venus,  and  Saturn,  are 
inclined  to  the  ecliptic  less  than  2°.  Saturn's  inclination 
is  2j°,  that  of  Venus  3|°,  and  Mercury's  7°,  as  in  the  dia- 
gram. Orbits  of  the  small  planets  stand  at  much  greater 
angles;  six  are  inclined  more  than  25°,  and  the  average 
of  the  group  is  about  8°.  The  two  opposite  points  where 
a  planet's  orbit  cuts  the  ecliptic  are  called  its  nodes. 

Eccentricity  of  their  Orbits. — The  eccentricity  of  Mer- 
cury is  \,  of  Mars  ^j,  of  Jupiter,  Saturn,  and  Uranus  about 
2^,  and  of  Venus  and  Neptune  very  slight.  The  chief 
effect  of  the  eccentricity  is  to  change  a  planet's  distance 
from  the  sun,  between  perihelion  and  aphelion;  and  to 
vary  the  speed  of  revolution  in  orbit.  At  top  of  next 
page  are  eccentricities  of  the  planetary  orbits,  together 
with  total  variation  of  distance  due  to  eccentricity. 

Some  of  the  small  planets  have  an  eccentricity  more  than  double 
that  of  Mercury  even,  so  that  their  perihelion  point  is  near  the  orbit 
of  Mars,  while  at  aphelion  they  wander  well  out  toward  the  path  of 


Synodic  Periods  325 

ECCENTRICITY  AND  VARIATION  OF  DISTANCE  FROM  THE  SUN 


ECCENTRICITY 

CHANGE  OF 

ECCENTRICITY 

CHANGE  OF 

DIST/ 

INCE  DUE  TO 

DISTANCE  DUE  TO 

ECCENTRICITY 

ECCENTRICITY 

Mercury, 
Venus, 

0.2056 
0.0068 

15 

Millions 
of 

Jupiter, 
Saturn, 

0.0482 
00561 

47 
90 

Millions 

>       of 

Earth, 
Mars, 

o.o  1  68 
0.0933 

3 
26  J 

miles 

Uranus, 
Neptune, 

0.0464 
0.0090 

1  66 
49  J 

miles 

Jupiter.  The  average  eccentricity  of  their  orbits  is  excessive,  being 
about  equal  to  that  of  Mercury.  The  path  of  Andromache  (175)  is 
very  like  the  orbit  of  Tempers  comet  n.  (page  401). 

Synodic  Periods.  —  Just  as  with  the  moon,  so  each 
planet  has  two  kinds  of  periods.  A  planet's  sidereal 
period  is  the  time  elapsed  while  it  is  journeying  once  com- 
pletely round  the  sun,  setting  out  from  conjunction  with 
some  fixed  star  and  returning  again  to  it.  If  during  this 
interval  the  earth  remained  stationary  as  related  to  the 
sun,  the  times  occupied  by  the  planets  in  traversing  the 
round  of  the  ecliptic  would  be  their  true  sidereal  periods. 
But  our  continual  eastward  motion,  and  the  apparent 
motion  of  sun  in  same  direction,  makes  it  necessary  to 
take  account  of  a  second  period  of  revolution  —  the 
synodic  period,  or  interval  between  successive  conjunc- 
tions. If  a  superior  planet,  the  average  interval  between 
oppositions  is  also  the  synodic  period.  Following  are  the 

SYNODIC  PERIODS 


THE  TERRESTRIAL  PLANETS 


THE  MAJOR  PLANETS 


Mercury n6days 

Venus 584  days 

Mars 780  days 


Jupiter 399  days 

Saturn 378  days 

Uranus 370  days 

Neptune 368  days 


326 


The  Planets 


The  exceptional  length  of  the  synodic  periods  of  Venus 
and  Mars  is  due  to  the  fact  that  their  average  daily  motion 
is  more  nearly  that  of  the  earth  than  is  the  case  with  any 
of  the  other  planets. 

Sidereal  Periods.  —  As  our  earth  is  a  moving  observa- 
tory, it  is  impossible  for  us  to  determine  the  sidereal 
periods  of  the  planets  directly  from  observation.  But  their 
synodic  periods  may  be  so  found ;  and  from  them  the  true 
or  sidereal  periods  are  ascertained  by  calculation,  involving 
only  the  relation  of  the  earth's  (or  sun's  apparent)  motion 
to  that  of  the  planet.  They  are  as  follows  :  — 

SIDEREAL  PERIODS  OR  PERIODIC  TIMES 


THE  TERRESTRIAL 

PLANETS 

THE 

MAJOR  PLANETS 

Mercury 

88   days 

Jupiter      . 

1  1  1  years 

Venus 

22  c    days 

Saturn  .     . 

2ol  years 

The  Earth 

36  c  4-  davs 

Uranus     • 

84    years 

Mars       

•     JW3?  uajrB 

.   687   days 

Neptune   . 

.  165    years 

Periodic  times  of  the  small  planets  range  between  three 
and  nine  years. 

Kepler's  Laws.  —  Kepler,  to  whom  the  motions  of  the 
planets  were  a  mystery,  nevertheless  had  discovered  in  1619 
three  laws  governing  their  motions.  (I)  the  orbit  of  every 
planet  is  elliptical  in  form,  and  the  sun  is  situated  at  one 
of  the  foci  of  the  ellipse.  (II)  The  motion  of  the  radius 
vector,  or  line  joining  the  planet  to  the  sun,  is  such  that 
it  sweeps  over  equal  areas  of  the  ellipse  in  equal  times. 
(Ill)  The  squares  of  the  periodic  times  of  the  planets 
are  proportional  to  the  cubes  of  their  average  distances 
from  the  sun.  Kepler  was  unable  to  give  any  physical  ex- 
planation of  these  laws.  He  merely  ascertained  that  all 
the  planets  appear  to  move  in  accordance  with  them. 


Distances  of  Planets  from  Sun  327 

Verification  of  Kepler's  Third  Law.  —  A  half  hour's  calculation  suf- 
fices to  prove  the  truth  of  this  law.  The  results  are  shown  in  the  last 
column  of  the  following  table,  where  the  number  in  each  line  was  ob- 
tained by  dividing  the  square  of  the  planet's  periodic  time  by  the  cube 
of  its  mean  distance  from  the  sun. 


VERIFICATION  OF  KEPLER'S  THIRD  LAW 


NAME  OF 
PLANET 

PERIODIC  TIME 
(IN  DAYS) 

MEAN  DISTANCE 
(EARTH'S  DISTANCE  =  i) 

[TIME]* 

[DISTANCE]3 

Mercury 

'  87.97 

0.3871 

133.414 

Venus 

224.70 

0.7233 

133430 

Earth 

365.26 

I  .OOOO 

I334I5 

Mars 

686.95 

1.5237 

133400 

Ceres 

1681.41 

2.7673 

133408 

Jupiter 

4332.58 

5.2028 

133.272 

Saturn 

10759.22 

9.5388 

133400 

Uranus 

30688.82 

I9-I833 

I334IO 

Neptune 

6oi8l.  II 

30.0551 

133403 

The  third  law  of  Kepler,  often  called  the  <  harmonic  law,'  is  rigorously 
exact,  only  upon  the  theory  that  planets  are  mere  particles,  or  exceed- 
ingly small  masses  relatively  to  the  sun.  On  this  account  the  discrep- 
ancy in  the  last  column  is  quite  large,  in  the  case  of  Jupiter,  because 
his  mass  is  nearly  T7XOIT  that  of  the  sun. 

Mean  Distances  of  the  Planets.  —  Kepler's  third  law  en- 
ables us  to  calculate  a  planet's  average  distance  from  the 
sun,  once  its  time  of  revolution  is  known ;  for  regarding 
the  earth's  period  of  revolution  as  unity  (one  year),  and 
our  distance  from  the  sun  as  unity,  it  is  only  necessary  to 
square  the  planet's  time  of  revolution,  extract  the  cube 
root  of  the  result,  and  we  have  the  planet's  mean  distance 
from  the  sun.  For  example,  the  periodic  time  of  Uranus 
is  84  years ;  its  square  is  7056 ;  the  cube  root  of  which  is 
19.18.  That  is,  the  mean  distance  of  Uranus  from  the  sun 
is  19.18  times  our  own  distance  from  that  central  luminary. 


328 


The  Planets 


Its  distance  in  miles,  then,  will  be  19.18  x  93,000,000.  In 
like  manner  may  be  found  the  distances  of  all  the  other 
planets  from  the  sun ;  and  they  are  as  follows  :  — 


MEAN  DISTANCE  FROM  THE  SUN 


THE 

TERRESTRIAL  PLANETS 

THE  MAJOR 

PLANETS 

Mercury  . 
Venus 

•      •      •      36^ 

Millions 

Jupiter    .... 
Saturn    .... 

4*3* 

886 

Millions 

of 

01 

of 

The  Earth 
Mars 

'      '      '      *k 

miles 

Uranus  .... 
Neptune      .     .     . 

1780 
2790    t 

miles 

_ 

These  distances  are  all  represented  in  true  relative  pro- 
portion in  the  figure  on  page  334.  Scattered  over  a  zone 
about  280  millions  of  miles  broad,  or  |  of  the  distance 
separating  Mars  from  Jupiter,  is  the  ring  of  small  planets, 
or  asteroids  probably  many  thousand  in  number,  of  which 
nearly  500  have  already  been  discovered. 

The  Nearest  and  the  Farthest  Planet.  —  Mars  is  often  said 
to  be  the  nearest  of  all  the  planets,  because  his  orbit  is  so 
eccentric  that  favorable  oppositions,  as  shown  later  in  the 
chapter,  may  bring  him  within  35,000,000  miles  of  the  earth. 
But  Venus  comes  even  nearer  than  that.  Her  distance 
from  the  sun  subtracted  from  ours  gives  26,000,000  miles 
for  the  average  distance  of  Venus  from  the  earth  at 
inferior  conjunctions ;  and  Venus  may  approach  almost 
2,000,000  miles  nearer  than  this,  if.  conjunction  comes  in 
December  or  January,  near  earth's  perihelion.  But  we 
must  not  think  of  Venus  as  being  proportionately  easier 
to  observe,  because  so  much  nearer.  It  might  even  be 
said  that  the  nearer  Venus  comes,  the  more  difficult  she 
is  to  observe,  because 'she  is  then  nearly  in  line  with  the 
sun,  whose  brightness  diffused  through  our  atmosphere 


Elements  of  Planetary  Orbits  329 

sets  a  serious  barrier  to  thorough  knowledge  of  her  surface. 
Of  the  known  planets  the  farthest  from  the  earth  is  Nep- 
tune. So  far  away  is  he  that  we  must  multiply  the  least 
distance  of  Venus  more  than  a  hundredfold  in  order  to 
obtain  the  distance  of  Neptune  from  the  earth. 

Aberration  Time.  —  Knowing  the  velocity  of  light  by  experiment, 
and  knowing  the  distances  of  the  planets  from  us,  it  is  easy  to  calcu- 
late the  time  consumed  by  light  in  traveling  from  any  planet  to  the 
earth.  So  distant  is  Neptune,  for  example,  that  light  takes  about 
4\  hours  to  reach  us  from  that  planet.  This  quantity  is  called  the 
planet's  aberration  time,  or  the  equation  of  light.  Its  value  in  seconds 
for  any  planet  is  equal  to  499  times  the  planet's  distance  from  the  earth 
(expressed  in  astronomical  units). 

Newton's  Law  of  Gravitation.  —  Sir  Isaac  Newton  about 
1675  simplified  the  three  laws  of  motion  of  the  planets 
into  a  single  law,  hence  known  as  the  Newtonian  law  of 
gravitation.  It  has  two  parts  of  which  the  first  is  this : 
that  every  particle  of  matter  in  the  universe  attracts  every 
other  particle  directly  as  its  mass  or  quantity  of  matter; 
and  second,  that  the  amount  of  this  attraction  increases 
in  proportion  as  the  square  of  the  distance  between  the 
bodies  decreases.  That  Kepler's  three  laws  are  embraced 
in  this  one  simple  law  of  Newton  may  be  shown  by  a 
mathematical  demonstration.  With  a  few  trifling  excep- 
tions, all  the  bodies  of  the  solar  system  move  in  exact  ac- 
cordance with  Newton's  law,  whether  planets  themselves, 
their  satellites,  or  the  comets  and  meteors.  Newton's  law 
is  often  called  'The  Law  of  Universal  Gravitation,'  be- 
cause it  appears  to  hold  good  in  stellar  space  as  well  as 
in  the  solar  system  itself. 

Elements  of  Planetary  Orbits.  —  The  mathematical  quan- 
tities which  determine  the  motion  of  a  celestial  body  are 
called  the  elements  of  its  orbit.  They  are  six  in  number, 
and  they  define  the  size  of  the  orbit,  its  shape,  and  its  rela- 
tion to  the  circles  and  points  of  the  celestial  sphere. 


330  The  Planets 

(1)  a  Mean  distance,  or  half  the  major  axis  of  the  ellipse 

in  which  the  planet  moves  round  the  sun. 

(2)  e  Eccentricity,  or  ratio  of  distance  between  center  and 

focus  of  ellipse  to  the  mean  distance. 

(3)  fl  Longitude  of  ascending  node,  or  arc  of  great  circle 

between  this  node  and  the  vernal  equinox. 

(4)  i  Inclination  of  plane  of  orbit  to  ecliptic. 

(5)  TT  Longitude  of  perihelion,  or  angle  between  line  of 

apsides  and  the  vernal  equinox. 

(6)  e  Longitude  of  the  planet  at  some  definite  instant,  often 

technically  called  the  epoch. 

Once  the  exact  elements  of  an  orbit  are  found,  the  undis- 
turbed motion  of  the  body  in  that  orbit  can  be  predicted, 
and  its  position  calculated  for  any  past  or  future  time. 

Secular  Variations  of  the  Elements.  —  About  a  century 
ago,  two  eminent  mathematical  astronomers  of  France, 
La  Grange  and  La  Place,  made  the  important  discovery 
that  the  action  of  gravitation  among  the  planets  can  never 
change  the  size  of  their  orbits ;  that  is,  the  element  a,  or 
the  mean  distance,  always  remains  the  same.  As  for  the 
other  elements  affecting  the  shape  of  the  orbit  and  its  posi- 
tion in  space,  they  can  only  oscillate  harmlessly  between 
certain  narrow  limits  in  very  long  periods  of  time.  These 
slow  and  minute  fluctuations  of  the  elements  are  called 
secular  variations ;  and  they  may  be  roughly  represented 
by  holding  a  flexible  and  nearly  circular  hoop  between  the 
hands,  now  and  then  compressing  it  slightly,  also  wobbling 
it  a  little,  and  at  the  same  time  slowly  moving  the  arms 
one  about  the  other.  The  oscillatory  character  of  the 
secular  variations  secures  the  permanence  and  stability 
of  our  solar  system,  so  long  as  it  is  not  subjected  to  per- 
turbing or  destructive  influences  from  without.  One  who 
really  wishes  fully  to  understand  these  complicated  rela- 


Variation  in  Apparent  Size  331 

tions  must  undertake  an  extended  course  of  mathematical 
study  —  the  only  master  key  to  complete  knowledge  of  the 
planetary  motions. 

Colors  —  Albedo  —  Bode  s  Law  —  Relative  Distances 

A  Planet  when  Nearest  looks  Largest.  —  In  proportion 
as  a  planet  comes  nearer  to  us,  its  apparent  disk  fills  a 


Variation  in  Apparent  Size  of  Mars 

larger  angle  in  the  telescope.  The  two  planets,  then, 
nearest  the  earth,  Venus  within  our  orbit,  and  Mars  with- 
out, must  undergo  the  greatest  changes  in  apparent  diame- 
ter, because  their  great- 
est distance  is  many 
times  their  least.  Mars, 
at  nearest  to  the  earth, 
is  35,000,000  miles  away ; 
at  farthest,  more  than 
seven  times  as  distant. 
This  seeming  variation 

.  .         ,  Variation  in  Apparent  Size  of  Venus 

in  size  is  shown  in  above 

figure.  The  next  greatest  variation  is  exhibited  by  Venus 
(lower  figure);  at  superior  conjunctions  she  seems  to  be 
only  one  sixth  as  large  as  at  inferior  conjunction. 

The  figure  illustrates  not  only  this  marked  increase  of  her  diameter  as 
she  comes  toward  us,  but  her  phases  also.     Third  in  order  is  Mercury, 


332  The  Planets 

whose  diameters  at  greatest  and  least  distance  are  about  as  i  to  3 
(already  shown  on  page  318).  And  following  Mercury  is  Jupiter, 
whose  variations  are  accurately  shown  in  the  adjacent  figure.  Saturn, 
Uranus,  and  Neptune,  too,  show  fluctuations  of  the  same  character, 
but  much  less,  because  of  their  very  great  distance  from  us.  From 

conjunction  to  opposition,  the 
apparent  breadth  of  Saturn  in- 
creases only  about  one  third ; 
while  the  similar  increase  of 
Uranus  and  Neptune  is  so 
slight  that  a  micrometer  is 
necessary  to  measure  it. 
Apparent  Magnitudes  and 

Variation  in  Apparent  Size  of  Jupiter  Colors     of     the     Planets.  —  All 

the  planets  .vary  in  bright- 
ness, as  their  distance  from  the  sun  and  the  earth  varies.  Five  of 
them  shine  with  an  average  brightness  exceeding  that  of  a  first 
magnitude  star.  Of  these,  Venus  is  by  far  the  brightest,  and  Jupiter 
next,  the  others  following  in  the  order  Mars,  Mercury,  and  Saturn. 
Uranus  is  about  equivalent  to  a  star  of  the  sixth  magnitude.  Also  a 
few  of  the  small  planets  approach  this  limit  when  near  opposition.  But 
Neptune's  vast  distance  from  both  sun  and  earth  renders  him  as  faint 
as  an  eighth  magnitude  star,  so  that  he  is  invisible  without  at  least  a 
small  telescope.  The  colors  of  the  planets  are  : 

Mercury,  pale  ash ; 
Venus,  brilliant  straw ; 
Mars,  reddish  ochre ; 
Jupiter,  bright  silver ; 
Saturn,  dull  yellow ; 
Uranus,  pale  green ; 
Neptune,  the  same. 

The  entire  significance  of  these  colors  is  not  yet  known ;  but 
apparently  they  are  indicant  as  to  degree  and  composition  of  atmos- 
phere enveloping  each. 

Albedo  of  the  Planets.  —  Albedo  is  a  term  used  to  express  the  capac- 
ity of  a  surface,  like  that  of  a  planet,  to  reflect  light.  It  is  a  number 
expressing  the  ratio  of  the  amount  of  light  reflected  from  a  surface  to 
the  amount  which  falls  upon  it.  By  observations  of  a  planet's  light 
with  a  photometer,  it  can  be  compared  with  a  star  or  another  planet, 
and  its  albedo  found  by  computation.  The  moon's  surface  reflects 
about  \  the  light  falling  upon  it  from  the  sun.  The  albedo  of  Mercury 
is  even  less,  or  \  ;  but  the  surface  of  Venus  is  highly  reflective,  its  albedo 


Distances  and  Motions  333 

being  \.  The  albedo  of  Mars  is  about  \  ;  that  of  Saturn  and  Neptune, 
about  the  same  as  Venus  ;  while  the  albedo  of  Jupiter  and  Uranus  is 
the  highest  of  all  the  planets,  or  nearly  \.  This  means  that  their  sur- 
faces reflect  about  four  times  as  much  light  as  sandstone  does. 

Ths  So-called  Law  of  Bode.  —  Titius  discovered  a  law  which  approxi- 
mately represents  the  relative  distances  of  the  planets  from  the  sun.  It 
is  derived  in  this  way.  Write  this  simple  series  of  numbers,  in  which 
each  except  the  second  is  double  the  one  before  it  : 

o  3  6  12  24  48  96 

Add  4  to  each,  giving 

4  7  10  16  28  52  100 

The  actual  distances  of  the  planets  known  in  the  time  of  Titius 
(1766)  are  as  follows  (the  earth's  distance  being  represented  by  10)  : 

39  7.2  10  15.2  52.0  95.4 


Although  the  law  is  by  no  means  exact,  Bode,  a  distinguished  Ger- 
man astronomer,  promulgated  it.  On  that  account  it  is  always  called 
Bode's  law.  Except  historically,  this  so-called  law  is  now  of  no 
importance  ;  for  its  error,  when  extended  to  the  outer  planets,  Uranus 
and  Neptune,  is  even  greater  than  in  the  case  of  Saturn.  But  by  direct- 
ing attention  to  a  break  in  succession  of  planets  between  Mars  and 
Jupiter,  Bode's  law  led  to  telescopic  search  for  a  supposed  missing 
body  ;  a  search  speedily  rewarded  by  discovery  of  the  first  four  small 
planets,  ©  Ceres,  ®  Pallas,  (3)  Juno,  and  @  Vesta. 

Relative  Distances  and  Orbital  Motions.  —  Once  the  distances  of  the 
planets  have  been  found,  measures  of  their  disks  with  the  telescope  en- 
able us  to  calculate  their  true  dimensions.  One  need  not  try  to  improve 
upon  Sir  John  HerscheFs  illustration  of  the  relative  distances,  sizes,  and 
motions  in  the  solar  system.  <  Choose  any  well-leveled  field  or  bowling 
green.  On  it  place  a  globe  two  feet  in  diameter  ;  this  will  represent  the 
sun  ;  Mercury  will  be  represented  by  a  grain  of  mustard  seed,  on  the 
circumference  of  a  circle  164  feet  in  diameter  for  its  orbit;  Venus  a  pea, 
on  a  circle  of  284  feet  in  diameter  ;  the  earth  also  a  pea,  on  a  circle  of 
430  feet  ;  Mars  a  rather  large  pin's  head,  on  a  circle  of  654  feet  ;  the 
asteroids,  grains  of  sand,  in  orbits  of  from  1000  to  1200  feet;  Jupiter 
a  moderate-sized  orange,  in  a  circle  nearly  half  a  mile  across  ;  Saturn  a 
small  orange,  on  a  circle  of  four  fifths  of  a  mile  ;  Uranus  a  full-sized 
cherry  or  small  plum,  upon  the  circumference  of  a  circle  more  than  a 
mile  and  a  half;  and  Neptune  a  good-sized  plum,  on  a  circle  about  two 
miles  and  a  half  in  diameter.  ...  To  imitate  the  motions  of  the 


334 


Relative  Distances 
and  Orbital  Motions 
of  the  Planets 


The  Planets 

planets,  in  the  above-mentioned  orbits,  Mercury 
must  describe  its  own  diameter  in  41  seconds ; 
Venus,  in  4m.  145. ;  the  earth,  in  7m.;  Mars,  in 
4  m.  48  s. ;  Jupiter,  in  2  h.  56  m. ;  Saturn,  in  3  h. 
13.  m. ;  Uranus,  in  2  h.  i6m.;  and  Neptune,  in 
3  h.  30  m.1  A  farther  and  helpful  idea  of  relative 
motion  of  the  planets  may  be  obtained  from  the  fig- 
ure, in  which  Mercury's  period  round  the  sun  is 
taken  as  the  unit.  While  he  is  moving  360°,  that  is 
in  88  days,  the  other  planets  move  over  the  arcs  set 
down  opposite  their  distance  from  the  sun.  This 
makes  very  apparent  how  much  the  motion  of  planets 
decreases  on  proceeding  outward  from  the  sun.  If 
Neptune  moves  as  an  athlete  runs,  Mercury  speeds 
round  with  the  celerity  of  a  modern  locomotive. 

Sizes  —  Masses  —  Axial  Rotation  —  Tidal 
Evolution 

The  Size  of  the  Planets.  —  Regarding 
the  group  of  small  planets  as  a  dividing 
line  in  the  solar  system,  all  planets  inside 
that  group  are,  as  previously  said,  rela- 
tively small,  and  all  outside  it  large.  The 
illustration  on  next  page  serves  to  show  this 
well,  presenting  not  only  the  relative  sizes 
of  the  planets,  but  also  the  relation  of 
their  diameters  to  the  sun's.  More  par- 
ticularly the  mean  diameters  are :  — 


Inner          ^rcury, 
Terrestrial  J  Venf  > 

Planets     |  Earth> 
(  Mars, 


3,000  miles 
7,700  miles 
7,920  miles 
4,200  miles 


Group  of  small  planets  :  Ceres  the  largest,  490 
miles  in  diameter. 

'     87,000  miles 

•  7i?oco  miles 

•  3^7oo  miles 
.     34,500  miles 


Outer    fJuPiter> 
Major  1  Saturn> 

Planets  |  Uranus> 
[  Neptune, 


Their  Masses  and  Densities  335 

Other  small  planets  whose  diam- 
eters have  been  measured  (by  Bar- 
nard) are  Pallas,  300  miles;  Juno,  (i^Jnt.) 
120  miles;  Vesta,  250  miles.  Prob- 
ably none  of  the  others  are  as 
large  as  Juno,  and  the  average  of  Uranus 

r    *  (4  satellites) 

recent  faint  discoveries  cannot  ex- 
ceed 20  miles. 


Masses  and  Densities  of  Planets.  —  Best 
by  comparison  can  some  idea  of  the  masses 
of  the  planets  be  conveyed.  Relative  Saturn 
weights  of  common  things  are  helpful,  and  (8  satellites) 
sufficiently  precise  :  Let  an  ordinary  bronze 
cent  piece  represent  the  earth.  So  small  are 
Mercury  and  Mars  that  we  have  no  coin 
light  enough  to  compare  with  them ;  but 
these  two  planets,  if  merged  into  a  single 
one,  might  be  well  represented  by  an  old- 
fashioned  silver  three-cent  piece;  Venus, 
by  a  silver  dime ;  Uranus,  a  silver  dollar, 
half  dollar,  and  quarter  together ;  Neptune, 
two  silver  dollars  ;  Saturn,  eleven  silver  dol- 
lars ;  and  Jupiter,  thirty-seven  silver  dollars  Jupiter 
(rather  more  than  two  pounds  avoirdupois) .  ^5  satellites) 
An  inconveniently  large  sum  of  silver  would 
be  required  if  this  comparison  were  to  be 
carried  farther,  so  as  to  include  the  sun ;  for 
he  is  nearly  750  times  more  massive  than 
all  the  planets  and  their  satellites  together, 
and,  on  the  same  scale  of  comparison,  he 
would  somewhat  exceed  the  weight  of  the  Mars  , 

&     .  ,      (2  satellites) 

long   ton.      In  striking  contrast  with  this 
vast  and  weighty  globe  are  the  tiny  asteroids,  Earth 
so  light  that  300  of  them  have  been  esti-  d  satellite) 
mated  to  have  a  mass  of  only  ^^  that  of 
our  earth.      If  we  derive  the  densities  of 
planets  as  usually,  by  dividing  mass  by  vol-  Mercurv 
ume,  we  find  that  Mercury  is  the  densest 
of  all  (one  fifth   denser  than  the  earth). 

Venus.  Earth,  and  Mars  come  next,  the  last      .    Relative  Sizes  of  Planets 

(Sun's  Diameter  on  Same  Scale 
equals  Length  of  the  Cut) 


Small 


336  The  Planets 

a  quarter  less  dense  than  our  globe.  Three  of  the  major  planets 
have  about  the  same  density  as  the  sun  himself;  that  is,  only  one  fourth 
part  that  of  the  earth.  Saturn^s  mean  density  is  the  least  of  all,  only 
one  eighth  that  of  our  globe. 

Center  of  Gravity  of  the  Sun  and  Jupiter.  —  Though 
the  sun's  mass  is  vastly  greater  than  that  of  his  entire 
retinue  of  planets  put  together,  he  is  nevertheless  forced 
appreciably  out  of  the  position  he  would  otherwise  occupy 

by  the   powerful   attrac- 
11      tion  of  the  giant  planet 
whose  mass  is  YQTT  his 
own.    It  is  easy  to  calcu- 

Jupiter  balancing  the  Sun  late    how    much      for    the 

sun  and  Jupiter  revolve  round  their  common  center  of 
gravity,  exactly  as  if  the  two  vast  globes,  5  and  J,  were 
connected  by  a  rigid  rod  of  steel.  But  as  5  weighs  1047 
times  as  much  as  /,  the  center  of  gravity  of  the  system 
is  yfl^-g-  of  the  distance  between  the  centers  of  5  and 
J.  Now  as  Jupiter  in  perihelion  makes  this  distance 
460,000,000  miles,  the  center  of  gravity  is  displaced  from 
6"  toward  J  440,000  miles.  But  the  radius  of  the  sun  is 
433,000  miles;  so  the  center  of  gravity  of  the  Sun-Jupiter 
system  is  never  less  than  7000  miles  outside  the  solar 
orb.  And  this  distance  becomes  greater  as  Jupiter  recedes 
to  his  aphelion. 

Axial  Rotation  of  the  Planets.  —  The  giant  planet  turns 
most  swiftly  on  his  axis,  for  the  average  period  of  rotation 
of  the  white  belt  girdling  his  equator  is  only  9  h.  50^  m. 
But,  like  the  sun,  his  zones  in  different  latitudes  revolve  in 
different  periods,  the  average  of  which  is  about  9  h.  55 \  m. 
The  period  of  revolution  of  the  great  red  spot  averages 
9  h.  55  m.  39  s.  Saturn,  too,  exhibits  similar  discrepancies, 
but  the  white  spots  of  his  equatorial  belts  gave,  in  1893,  a 
period  of  10  h.  12  m.  53  s.  There  are  indications  that  the 


Their  Librations  337 

axial  period  of  Uranus  is  about  the  same ;  but  that  of 
Neptune  is  unknown.  Next  in  order  of  length  is  Mars, 
whose  day  is  equal  to  24  h.  37  m.  22.7  s.,  a  constant  known 
with  great  precision,  because  it  has  been  determined  by 
observing  fixed  markings  upon  the  surface,  and  the  whole 
number  of  revolutions  is  many  thousand.  Then  comes 
our  earth  with  its  day  of  23  h.  56  m.  4.09  s.  Following, 
though  at  a  long  distance,  are  Mercury  and  Venus,  which 
turn  round  but  once  on  their  axes  while  going  once  round 
the  sun.  The  axial  period  (sidereal)  of  the  former,  then 
is  88  days;  and  of  the  latter,  225  days,  —  the  longest 
known  in  the  solar  system.  Her  solar  day,  therefore,  is 
infinite  in  duration,  and  her  year  and  sidereal  day  are  equal 
in  length.  This  equality  of  periods,  in  both  Mercury  and 
Venus,  was  undoubtedly  effected  early  in  their  life  history, 
through  the  agency  of  friction  of  strong  sun-raised  tides 
in  their  masses,  then  plastic. 

Ellipticity  and  Axial  Inclination  of  the  Planets. —  The  disks  of 
many  of  the  planets  do  not  appear  perfectly  circular,  but  exhibit  a 
degree  of  flattening  at  the  poles.  This  is  due  to  rotation  about  their 
axes,  the  centrifugal  force  producing  an  equatorial  bulge.  In  the  case 
of  Jupiter  and  Saturn,  it  is  so  marked  as  to  attract  immediate  attention 
on  examining  their  disks  with  the  telescope.  The  polar  flattening 
of  Saturn's  ball  is  \  (page  367),  of  Uranus  ^  and  of  Jupiter  T^ 
(page  363),  these  planets  being  exceptionally  large,  and  their  axial 
rotation  relatively  swift.  Next  comes  Mars,  whose  polar  flattening  is 
T&3,  followed  by  the  earth's,  ^n.  The  ellipticity  of  the  other  planets, 
of  the  satellites,  and  of  the  sun  itself,  is  so  small  as  to  escape  detection. 
Inclination  of  planetary  equator  to  plane  of  orbit  round  the  sun  is  ex- 
cessive in  the  case  of  Uranus  ;  also  probably  in  Neptune  ;  has  a  medium 
value  (about  25°)  for  the  earth,  Mars,  and  Saturn ;  and  is  very  slight 
for  all  the  other  three  great  planets. 

Librations   of   the    Planets.  — There   are   librations   of 

planets,  just  as  there  are  librations   of   the   moon.     But 

the  only  planetary  libration  we  need  to  consider  is  libration 

in  longitude.    This  is  due  to  the  fact  that,  while  the  planet 

TODD'S  ASTRON.  —  22 


338  The  Planets 

turns  with  perfect  uniformity  on  its  axis,  its  revolution  in 
orbit  is  swifter  near  perihelion,  and  slower  near  aphelion 
than  the  average.  The  amount  of  a  planet's  libration  in 
longitude,  therefore,  will  depend  upon  the  degree  of  eccen- 
tricity of  its  orbit ;  and  it  must  be  taken  into  account  in 
finding  the  true  period  of  the  planet's  day. 

Mercury's  libration  is  the  greatest  of  all.  His  average  daily  angle  of 
rotation  is  about  4° ;  but  at  perihelion  he  moves  round  the  sun  more 
than  6°,  and  at  aphelion  rather  less  than  3°  daily.  The  effect  of  libra- 
tion is  an  apparent  oscillation  of  the  disk,  alternately  to  the  east  and 
west.  Starting  from  perihelion,  the  angle  of  revolution  in  orbit 
gains  about  2°  each  day  on  the  angle  of  axial  turning ;  the  amount  of 
gain  constantly  diminishing,  until  nearly  three  weeks  past  perihelion. 
Mercury's  libration  is  then  at  its  maximum,  amounting  to  23^°  at 
the  center  of  the  disk.  In  the  opposite  part  of  his  orbit,  the  disk 
seems  to  swing  as  much  in  the  opposite  direction,  making  thus  the 
extent  of  the  angle  of  Mercury's  libration  equal  to  47°.  On  \  of 
his  surface,  then,  the  sun  never  shines.  On  \  it  is  perpetually 
shining,  and  on  \  there  is  alternate  sunshine  and  shadow.  So,  too, 
on  Mars,  there  is  an  apparent  libration  of  the  center  of  the  disk, 
though  not  so  large  as  Mercury's,  because  his  orbit  is  less  elliptical ; 
and  the  sun  shines  on  every  part  of  the  surface,  because  the  rotation 
and  revolution  periods  of  Mars  are  not  equal.  Still  less  are  the  libra- 
tions  of  Jupiter  and  Saturn,  their  eccentricity  of  orbit  being  only 
about  half  that  of  Mars. 

Tidal  Evolution.  —  By  tidal  evolution  is  meant  the  dis- 
tinct role  played  by  tides  in  the  progressive  development 
of  worlds.  The  term  tide  is  here  used,  not  in  its  common 
or  restricted  sense,  applying  to  waters  of  the  ocean,  but  to 
that  periodic  elevation  of  plastic  material  of  a  world  in  its 
early  stages,  occasioned  by  gravitation  of  an  exterior  mass. 
Newton's  law  of  gravitation  first  gave  a  full  explanation 
of  the  rising  and  falling  of  ocean  tides,  but  as  applied  to 
motions  of  planets,  it  presupposed  that  all  these  bodies 
were  rigid.  In  1877,  George  Darwin,  in  a  series  of  elabo- 
rate mathematical  papers,  showed  the  effect  of  gravitation 
upon  these  masses  in  earlier  stages  of  their  history,  whenj 


Transits  of  Inferior  Planets  339 

according  to  the  nebular  hypothesis,  they  were  not  rigid, 
but  composed  of  yielding  material.  Ocean  tides  are  raised 
at  the  gradual,  though  almost  inappreciable,  expense  of 
earth's  energy  of  rotation.  In  like  manner,  earth-raised 
tides  in  the  youthful  moon  continued  to  check  its  axial 
rotation  until  that  effect  was  completely  exhausted,  and 
the  moon  has  never  since  turned  on  its  axis  relatively  to 
the  earth.  Evidently  this  effect  of  tidal  friction  has  been 
operant  in  the  case  of  sun-raised  tides  upon  the  planets, 
—  more  powerfully  if  the  planet  is  nearer  the  sun;  less 
powerfully  if  its  mass  is  great ;  also  less  powerfully  if  its 
materials  have  early  become  solidified  on  account  of  the 
planet's  small  size.  Combination  of  these  conditions  ex- 
plains the  present  periods  of  rotation  of  all  the  planets : 
Mercury  and  Venus  strongly  acted  upon  by  the  sun,  so 
that  they  now  and  for  all  time  turn  their  constant  face 
toward  him  ;  earth,  also  probably  Mars,  even  yet  suffer- 
ing a  very  slight  lengthening  of  their  day ;  Jupiter  and 
Saturn,  also  probably  Uranus  and  Neptune,  still  endowed 
with  swift  axial  rotation,  because  of  ( I )  their  massiveness, 
and  (2)  their  vast  distance  from  the  center  of  attraction. 


Transits —  Satellites  —  Atmospheres  —  Surfaces 

Transits  of  Inferior  Planets.  —  If  either  Mercury  or 
Venus  at  inferior  conjunction  is  near  the  node  of  the  orbit, 
the  planet  can  be  seen  to  pass  across  the  sun  like  a  round 
black  spot.  This  is  called  a  transit.  About  13  transits 
of  Mercury  take  place  every  century,  the  shortest  interval 
being  3^  years,  and  the  longest  13.  They  can  happen 
only  in  the  early  part  of  May  and  November,  because  the 
earth  is  then  near  the  nodes  of  Mercury's  orbit.  There 
are  about  twice  as  many  transits  in  November  as  in  May, 
because  Mercury's  least  distance  from  the  sun  falls  near 


340 


The  Planets 


the  November  node.  Transits  of  Venus  occur  in  pairs, 
eight  years  apart ;  and  the  intervals  between  the  midway 
points  of  the  pairs  are  alternately  U3|-  and  I2QJ  years. 
June  and  December  are  the  only  possible  months  for  their 
occurrence,  and  a  June  pair  in  one  century  will  be  fol- 
lowed by  a  December  pair  in  the  next.  Both  Mercury 
and  Venus  at  transit,  being  then  nearest  the  earth,  their 
apparent  motion  is  westerly  or  retrograde.  Consequently 
a  transit  always  begins  on  the  east  side 
of  the  sun.  Duration  of  transit  varies 
with  the  part  of  the  disk  upon  which 
the  planet  seems  to  be  projected, 
whether  north  or  south  of  the  center 
or  directly  over  the  middle. 

Contacts  at  Ingress  and  Egress.  —  Hold  the 
book  up  south.  The  white  arc  in  the  figure 
adjacent  will  then  represent  the  east  limb  of 
the  sun,  upon  which  the  planet  enters  at  in- 
gress, or  beginning  of  transit,  as  seen  in  an 
ordinary  astronomical  telescope.  Upper  part 
of  figure  shows  the  phase  called  external 
contact.  Actual  geometric  contact  cannot  of 
course  be  observed,  because  it  is  impossible 
to  see  the  planet  until  its  edge  has  made  a 
slight  notch  into  the  sun's  limb.  The  ob- 
server catches  sight  of  this  as  soon  as  possi- 
ble, and  records  the  time  as  his  observation 
of  external  contact.  The  planet  then  moves 
along  to  the  left,  until  it  reaches  the  phase 
shown  at  I,  a  few  seconds  before  internal 
contact.  The  observer  must  then  watch 

intently  the  bright  horns,  which  will  soon  close  in  rapidly  toward  each 
other,  and  finally  a  narrow  filament  of  light  will  shoot  quickly  across 
and  join  the  two  horns  together.  This  will  be  internal  contact  shown 
at  II.  After  a  few  seconds  the  planet  will  have  advanced  to  III,  well 
within  the  limb  of  the  sun.  Then  there  will  be  little  to  observe  until 
the  planet  has  crossed  the  solar  disk,  and  is  about  to  present  the 
phases  of  egress.  These  will  be  exactly  similar  to  those  at  ingress, 
but  will  take  place  in  reverse  order.  The  atmosphere  of  Venus  (page 


Contacts  at  Ingress 


Transits  of  Mercury 


341 


348)  complicates  observations  of  these  contacts,  and  they  cannot  be 
observed  within  two  or  three  seconds  of  time. 

Past  and  Future  Transits  of  Mercury.  —  Gassendi  made  the  first 
observation  of  a  transit  of  Mercury  in  1631.  The  annexed  engraving 
shows  the  paths  of  Mercury  during  all  transits  from  1868  to  1924. 


Paths  of  Transits  Of  Mercury  at  Ascending  and  Descending  Nodes 

The  circle  represents  the  disk  of  the  sun ;  near  the  top  is  north,  and 
below  the  right  side  west.  The  broken  line  is  part  of  the  ecliptic.  Con- 
sider first  the  November  transits.  Their  dates  are  :  5th  November,  1868  ; 
7th  November,  1881  ;  loth  November,  1894;  I2th  November,  1907  ;  6th 
November,  1914.  Mercury  is  then  near  ascending  node;  and  the 
paths  of  these  transits  are  drawn  at  an  ascending  angle  of  about  7°  to 
the  ecliptic,  this  being  the  inclination  of  Mercury's  orbit  to  that  plane. 
Dots  on  these  paths  show  positions  at  half-hour  intervals.  Observe 
how  far  apart  they  are.  This  is  because  Mercury  is  near  perihelion, 
where  swifter  motion,;  carries  him  quickly  across  the  sun.  Next,  con- 
sider the  May  transits.  They  are  only  three  in  number  in  the  same 
interval,  and  their  dates  are:  6th  May,  1878;  9th  May,  1891;  7th 


342 


The  Planets 


May,  1924.  They  occur  near  Mercury's  descending  node,  as  shown, 
that  of  1924  being  nearly  central  because  Mercury  happens  to  come  to 
inferior  conjunction  with  the  earth,  at  very  nearly  the  time  of  reaching 
its  node.  The  half-hour  dots  are  nearer  together  than  in  November 
transits,  because  Mercury  is  near  aphelion,  and  consequently  his  motion 
is  as  slow  as  possible.  The  greatest  length  of  a  transit  of  Mercury 
is  7  h.  50  m.,  and  the  transit  of  1924  approaches  near  this  limit. 

Past  and  Future  Transits  of  Venus.  —  Jeremiah  Horrox  made  the 
first  observation  of  a  transit  of  Venus  in  1639.  Nearly  every  century 
witnesses  a  pair  of  these  transits.  Below  are  four  disks  representing 


Paths  of  Transits  of  Venus  at  Ascending  and  Descending  Nodes 

the  sun ;  and  upon  them  are  indicated  apparent  paths  of  Venus,  for 
all  transits  occurring  in  the  ijth  to  the  2ist  centuries  inclusive.  In  each 
case  the  top  of  the  disk  is  north,  and  the  right-hand  side  west.  The 
dots  show  the  position  of  the  planet  at  intervals  of  fifteen  minutes. 
Pairs  of  transits  take  place  at  average  intervals  of  i  \  centuries  ;  so  there 
will  be  no  transit  of  Venus  in  the  2oth  century. 


DATES  OF  TRANSITS  OF  VENUS 


AT  THE  ASCENDING  NODE 

AT  THE  DESCENDING  NODE 

1631,  December  7 
1639,  December  4 
1874,  December  9 
1882,  December  6 

1761,  June  5 
1769,  June  3 
2004,  June  8 
2012,  June  6 

As  is  evident  from  the  figure,  a  pair  of  transits  at  ascending  node 
(1631  and  1639)  is  followed  by  a  pair  at  descending  node  (1761  and 
1769),  and  so  on  alternately.  Southern  transits  at  ascending  node 
(1639  and  1882)  are  followed  by  southern  transits  at  descending  node 


Their  Satellites  343 

(1761  and  2004)  ;  and  a  northern  transit  at  descending  node  (1769)  is 
followed  by  a  northern  transit  at  ascending  node.  Rows  of  black  dots 
in  contact  with  each  other  indicate  the  chord  of  the  sun's  disk  traversed 
at  each  transit,  as  seen  from  the  center  of  the  earth.  The  greatest 
possible  length  of  a  transit  of  Venus  is  7  h.  58  m.,  and  the  shortest 
one  ever  observed  was  that  of  1874.  Transits  of  Venus  are  phe- 
nomena of  great  interest  to  astronomers,  because  proximity  of  the 
planet  produces  a  large  effect  of  parallax.  By  measuring  it,  her  dis- 
tance from  the  earth  is  found.  This  tells  us  the  scale  on  which  the 
solar  system  is  built,  including  therefore  the  length  of  the  unit  in 
astronomical  measures,  the  sun's  mean  distance  from  the  earth.  The 
transits  of  1769  and  1882  were  visible  in  the  United  States.  Those  of 
1874  and  1882  were  extensively  observed  by  costly  expeditions  under 
the  auspices  of  the  principal  governments. 

Satellites  of  the  Planets 

Satellites  of  the  Terrestrial  Planets.  —  The  solar  system 
has  this  curious  and  interesting  feature,  that  most  of  its 
chief  planets  are  accompanied  by  moons  or  satellites. 
Twenty-one  are  now  known.  No  satellite  has  yet  been 
discovered  belonging  to  either  of  the  inferior  planets. 
There  have,  however,  been  many  spurious  observations  of 
a  supposed  satellite  of  Venus.  Our  earth  has  but  one. 
Mars  has  two  satellites,  discovered  by  Hall  in  1877.  They 
are  about  seven  miles  in  diameter,  and  can  be  seen  only  by 
large  telescopes  under  favorable  conditions.  Phobos,  the 
inner  moon  of  Mars,  is  less  than  4000  miles  from  the  planet's 
surface,  and  travels  round  in  7  h.  39  m.,  a  period  less  than 
one  third  that  of  Mars'  rotation.  To  an  observer  on  the 
planet,  Phobos  must,  therefore,  seem  to  rise  in  the  west 
and  set  in  the  east.  Its  horizontal  parallax  is  enormous, 
being  2i£°.  The  outer  moon,  Deimos,  is  rather  more  than 
12,000  miles  from  the  surface  of  Mars,  and  its  periodic 
time  is  30  h.  i8m.  As  the  planet's  day  is  24  h.  37m., 
Deimos  must  consume,  allowing  for  parallax,  about  2\ 
days  in  leisurely  circuiting  the  Arean  sky  from  horizon 
to  horizon. 


344 


The  Planets 


Satellites  of  the  Major  Planets.  —  Jupiter,  has  five  moons, 
the  fifth  or  innermost  discovered  only  in  1892  by  Barnard. 
The  four  large  ones  were  discovered  by  Galileo  in  1610 
with  the  first  telescope  ever  used  astronomically.  The 
orbits  of  Jupiter's  moons  lying  nearly  in.  the  ecliptic  are 
always  seen  edgewise,  or  very  nearly,  so  that  the  satellites 
in  traveling  round  the  primary  seem  merely  to  oscillate 
forth  and  back,  just  as  the  pedals  of  a  distant  bicycle, 
moving  toward  or  from  us,  seem  simply  to  rise  and  fall. 
Saturn  is  very  rich  in  attendants,  having  not  only  the 
wonderful  rings  (quite  different  from  everything  else  in 
the  solar  system,  and  undoubtedly  made  up  of  an  infinity 
of  small  individual  bodies  or  satellites,  too  small  ever  to 
be  separately  seen),  but  in  addition  eight  distinct  satellites 
are  known.  Uranus  has  four  moons,  and  far-away  Nep- 
tune has  one  attendant  body.  The  paths  of  all  these 
satellites  are  nearly  circular,  except  those  of  our  moon  and 
Hyperion. 

Periods,  Transits,  Occultations,  and  Eclipses.  —  Following 
are  the  principal  data  of  the  satellites  of  Jupiter :  — 


THE  SATELLITES  OF  JUPITER 


NUM- 
BER 

DIAMETER 

DISTANCE  FROM 
JUPITER 

SIDEREAL  PERIOD  OF 
REVOLUTION 

MASS  IN 
TERMS  OF 
JUPITER 

V 

ioo  miles 

1  1  2,000  miles 

0 

d.  ii  h.  57  m.  22.7  s. 

? 

I 

2500 

261,000 

I 

18       27       33.5 

sUffff 

II 

2100 

415,000 

3 

13       13       42.1 

?TooF 

III 

3600 

664,000 

7 

3       42       334 

TToffff 

IV 

3000 

1.167.000 

16 

16      32        ii.  2 

^ 

So  near  Jupiter  is  the  fifth  satellite  that  his  disk,  as  seen  from  the 
surface  of  the  satellite,  would  stretch  more  than  half  way  from  horizon 
to  zenith.  Referring  to  conditions  which  produce  eclipses  of  sun  and 


Light  Requires   Time  to   Travel  345 


moon,  illustrated  on  page  293,  and  remembering  that  the  orbits  of 

Jupiter's  satellites  nearly  coincide  with  the 

plane  of  his  path,  it  is  clear  that  eclipses  of 

the  sun  and  of  Jupiter's  moons  must  occur 

every  time  a  satellite  goes  round  the  planet. 

So  there  are   nearly   9000   eclipses   of  the 

sun  and  moons  annually,  from  some  point 

or  other  of  Jupiter's  disk.     The  iv  satellite 

alone  escapes  eclipse  —  about  half  the  time. 

When  the   dark   shadow   of  a   satellite   is 

seen  to  cross  the  disk,  it  is  called  a  transit 

of  the  shadow ;   and  the  projection  of  the 

satellite  itself  on  the  disk  is  called  a  transit  of 

the  satellite.     In  the  opposite  part  of  their 

orbits,  a  satellite's  passing  behind  the  disk  is  called  an  occultation ; 

and  its  dropping  into  the  planet's  shadow  is  called  an  eclipse.     Eclipses 

vary  from  just  a  few  minutes  to  nearly  five  hours  in  length.     Eclipses, 

occultations,  and  transits  are  predicted  many  years  in  advance  in  the 

Epheineris,  and  are  very  interesting  to  observe,  even  with  small  tele- 
scopes. An  opera  glass  will  show  at  a  glance  the  moons  which  are  not 
in  transit,  occultation,  or  eclipse.  Sometimes  all  four  dis- 
appear for  a  time,  though  not  again  in  the  I9th  century. 


Jupiter  (Shadow  of  Satellite  in 
Transit) 


Light    requires   Time  to   travel.  —  In    1675, 
Roemer  first  suspected  this,  because  he  found 
that  when   Jupiter  was  in    opposition,  eclipses 
of    his  satellites   took    place    several    minutes 
earlier  than  the  average,  and  when  in  conjunc- 
tion, the  same  amount  later.     The  figure  shows 
why;   for  when  Jupiter  is  in  conjunction,  sun- 
light reflected  from  a  satellite  must  journey  an 
•^g^-     entire    diameter   of    the    earth's    orbit^  farther 
(JEumE™N      than  at  opposition.     Eclipses  of  all  four  moons 
exhibited  the    same  discrepancy.     So  the  con- 
clusion was  manifest,  that  light  requires  a  definite  time  to 
travel ;    and  we    now  know,  from  elaborate  calculations, 
that   light   from   these   moons   travels    across   the   earth's 
orbit   in   998   seconds.     Half  this  number,  or  499,  is  the 
constant    factor    in    'the  equation    of  light.'       Its  careful 


34^ 


The  Planets 


determination  is  a  matter  of  great  importance,  and  eclipses 
of  Jupiter's  satellites  are  now  recorded  with  high  accuracy 
by  the  photometer  and  by  means  of  photography. 

Physical  Peculiarities  of  Jupiter's  Satellites.  —  The  first  satellite  is 

not  a  sphere,  but  a  prolate 
ellipsoid,  its  longer  axis  being 
directed  toward  the  center  of 
Jupiter  —  a  remarkable  peculi- 
arity discovered  by  W.  H .  Pick- 
ering and  verified  by  Doug- 
lass. Markings,  very  faint  in 
character,  have  been  seen  upon 

Markings  on  Jupiter's  3d  Satellite  (Douglass)       a11  the  satellites.      By  means  of 

these  their  periods  ot  axial  rev- 
olution are  found.  Fading  out  at  the  edge  may  be  indication  that  in 
possesses  an  atmosphere.  Satellites  in  and  iv,  also  probably  I  and  11, 
turn  round  once  on  their  axes  while  going  once  round  Jupiter,  a  rela- 
tion like  that  of  our  moon  to  the  earth.  Douglass,  from  observations 
of  very  narrow  belts  on  in  in  1897,  makes  its  period  of  rotation  7  d.  5  h 
Also  he  has  published  the  adjoining  sketch-map  of  the  satellite's  sur 
face.  Near  the  poles  of  in  and  iv  white  spots  have  been  seen  by  sev- 
eral observers. 

Satellites  of  Saturn.  —  Following  are  the  principal  data 
of  the  satellites  of  Saturn  : — 


THE  SATELLITES  OF  SATURN 


NUM- 
BER 

NAME  OF 
SATELLITE 

NAME  OF 
DISCOVERER 

DATE  OF 
DISCOVERY 

DIAMETER 

DISTANCE 

FROM 

SATURN 

SIDEREAL 
PERIOD  OF 
REVOLUTION 

. 

miles 

miles 

d.    h.   m.     s. 

I 

Mimas 

W.  Herschel 

17  Sept.  1789 

750 

117,000 

o  22  37     5.7 

II 

Enceladus 

W.  Herschel 

28  Aug.  1789 

800 

157,000 

i     8  53     6.9 

III 

Tethys 

J.  D.  Cassini 

21  Mar.  1684 

IIOO 

186,000 

I  21   18  25.6 

IV 

Dione 

J.  D.  Cassini 

21  Mar.  1684 

I2OO 

238,000 

2  17  41     9.3 

V 

Rhea 

J.  D.  Cassini 

23  Dec.  1672 

IS°° 

332,000 

4  12  25  n.6 

VI 

Titan 

C.  Huygens 

25  Mar.  1655 

3500 

771,000 

15    22    41    23.2 

VII 

Hyperion 

W.  C.  Bond 

16  Sept.  1848 

500 

934,000 

21     6  39  27.0 

VIII 

lapetus 

J.  D.  Cassini 

25  Oct.  1671 

2000 

2,225,000 

79    7  54  17.1 

Satellite  of  Neptune 


347 


The  orbits  of  the  five  inner  satellites  are  circular.  The 
satellites  first  discovered  are  easiest  to  see,  the  largest, 
Titan,  being  nearly  always  visible  even  with  very  small 
instruments.  Its  mass  according  to  Stone  is  -^gVo"  t^lat  °^ 
Saturn.  Eclipses  and  transits  of  some  of  the  satellites 
have  occasionally  been  observed  with  large  telescopes. 

Satellites  of  Uranus.  —  Following  are  the  principal  data 
of  the  satellites  of  Uranus  :  — 


THE  SATELLITES  OF  URANUS 


NUMBER 

NAME  OF 
SATELLITE 

DISTANCE  FROM 
URANUS 

SIDEREAL  PERIOD 

OF  REVOLUTION 

I 

Ariel 

120,000  miles 

2d. 

12  h. 

29111. 

21.  1  S. 

II 

Umbriel 

167,000 

4 

3 

27 

37-2 

III 

Titania 

273,000 

8 

16 

56 

29.5 

IV 

Oberon 

365,000 

13 

ii 

7 

64 

The  two  inner  satellites  are  about  500  miles  in  diameter, 
and  the  outer  ones  are  nearly  twice  as  large.  For  the  next 
fifteen  years,  while  the  earth  is  near  a  line  perpendicular 
to  their  orbits,  the  satellites  may  always  be  seen  whenever 
Uranus  is  visible.  Only  great  telescopes,  however,  will 
show  them.  The  satellites  of  Uranus  revolve  in  planes 
nearly  at  right  angles  to  the  planet's  orbit,  and  their 
motion  is  retrograde,  or  from  east  to  west.  Ariel  and 
Umbriel  were  discovered  by  Lassell  in  1851  ;  Titania  and 
Oberon,  by  Sir  William  Herschel  in  1787. 

Satellite  of  Neptune.  —  Its  distance  from  Neptune  is 
224,000  miles,  the  period  of  revolution  5  d.  21  h.  3  m.,  with 
motion  retrograde.  It  was  discovered  by  Lassell  in  1846, 
only  a  few  weeks  after  the  planet  itself  was  found.  Prob- 
ably Neptune's  satellite  is  about  the  size  of  our  own  moon. 


348 


The  Planets 


Atmospheres  of  the  Planets 

Atmosphere  of  Mercury.  —  Without  much  doubt,  the 
atmosphere  of  Mercury  is  inappreciable.  His  color  by 
day,  when  best  observable,  resembles  that  of  the  pale  moon 
under  like  conditions.  If  there  is  no  air,  then  quite  cer- 
tainly no  water ;  as  evaporation  would  continue  to  supply 
a  slight  atmosphere  as  long  as  it  lasted.  The  .improba- 
bility of  an  atmosphere  surrounding  this  planet  is  con- 
firmed by  the  argument  from  the  kinetic  theory  of  gases, 
already  stated  (page  244);  for  Mercury's  mass  is  too  slight 
to  retain  an  envelope  of  aqueous  vapor. 

Atmosphere  of  Venus.  —  Observations  of  Venus  when 
very  near  her  inferior  conjunction  prove  the  existence  of 

an  atmosphere  which  is  thought 
to  be  more  dense  than  ours.  The 
illustration  shows  part  of  the  evi- 
dence:  Venus  is  just  entering 
upon  the  sun's  disk  during  the 
transit  of  1882,  and  sunlight  shin- 
ing through  the  planet's  atmos- 
phere illuminates  it  in  a  nearly 
complete  ring  surrounding  Venus, 
which  appears  dark  because  her 
sunward  side  is  turned  away  from 
us.  Also  an  aureole  surrounds 
the  dark  disk  when  in  transit ;  and 


has  passed  close  above  or  below 
the  sun  at  inferior  conjunction,  just  escaping  a  transit, 
the  horns  of  the  atmospheric  ring  have  been  observed 
almost  to  meet,  forming  a  nearly  complete  ring.  This 
crescent  would  be  little  more  than  a  complete  semicircle, 
if  there  were  no  atmosphere. 


Atmospheres  of  the  Planets  349 

Atmosphere  of  Mars.  —  Doubtless  a  thin  atmosphere  en- 
velops this  planet,  although  neither  so  extensive  nor  so 
dense  as  our  own.  While  usually  cloudless,  occasional  and 
temporary  veilings  of  some  of  the  best  known  regions  of 
the  planet  have  been  seen.  Many  careful  investigators, 
using  the  spectroscope,  have  found  absorption  lines  in  the 
spectrum  of  Mars  thought  to  be  due  to  neither  solar  nor 
terrestrial  atmosphere,  indicating  water  vapor  in  a  gas- 
eous envelope.  Also  regular  shrinking  and  subsequent 
enlarging  of  the  polar  caps  are  excellent  evidence  that  the 
ruddy  planet  is  surrounded  by  a  medium  acting  as  an 
agent  in  the  formation  and  deposition  of  snow.  Chang- 
ing intensity  of  the  light,  with  a  change  of  the  planet's 
phase  also  indicates  the  presence  of  an  atmosphere. 
Another  important  piece  of  evidence  is  the  discovery  of  a 
twilight  arc  of  about  12°,  causing  a  regular  increase  of  the 
planet's  apparent  diameter  through  the  equator,  as  phase 
increases.  Quite  certainly  density  of  the  atmosphere  of 
Mars  cannot  exceed  one  half  that  of  our  own,  and  prob- 
ably it  is  very  much  less.  Referring  again  to  the  kinetic 
theory  of  gases,  and  calculating  the  critical  velocity  for 
Mars,  we  find  it  to  be  rather  more  than  three  miles  per 
second.  Free  hydrogen,  then,  could  not  be  present  in  his 
atmosphere,  but  other  gases  might.  Campbell  and  Keeler 
have  found  the  spectrum  of  Mars  practically  identical  with 
that  of  the  moon,  indicating  probably  that  the  spectro- 
scopic  method  is  inconclusive. 

Atmosphere  of  Jupiter  and  Saturn.  — The  indications  of  a 
dense  and  very  extended  atmosphere  encircling  Jupiter 
are  unmistakable  :  —  ceaseless  changes  in  markings  called 
belts  and  spots ;  varying  length  of  the  planet's  day  in  dif- 
ferent regions  of  latitude ;  absorption  shadings  in  the  in- 
ferior portion  of  Jupiter's  spectrum ;  and  withal  his  giant 
mass  potent  to  -retain  captive  all  gaseous  materials  origi- 


350  The  Planets 

nally  belonging  to  him.  Probably  in  point  of  both  depth 
and  chemical  constitution,  the  atmosphere  of  Jupiter  is 
widely  diverse  from  our  own ;  in  fact,  it  is  not  unlikely 
that  this  great  planet  may  still  be  in  a  gaseous  condi- 
tion throughout.  At  least  the  depth  of  atmosphere  must 
be  reckoned  in  thousands  of  miles.  Dark  bands  in  the 
red  may  be  due  to  some  substance  in  the  planet's  at- 
mosphere not  in  our  own,  and  possibly  metallic.  In 
nearly  every  respect  the  atmosphere  of  the  ball  of  Saturn 
resembles  that  of  Jupiter,  but  the  ring  gives  every  appear- 
ance of  being  without  atmosphere.  Saturn's  spectrum,  too, 
is  quite  the  same  as  Jupiter's,  and  its  intenser  absorption 
bands  indicate  a  little  more  plainly  the  presence  of  gaseous 
elements  as  yet  unrecognized  on  the  earth  and  in  the 
sun.  Another  indication  of  atmosphere,  common  to  both 
these  planets,  is  the  shading  out  or  absorption  of  all  mark- 
ings at  the  limb  or  edge  of  their  disks. 

Atmosphere  of  Uranus  and  Neptune.  —  So  remote  are 
these  planets,  and  so  small  their  apparent  disks,  that  practi- 
cally nothing  has  yet  been  ascertained  concerning  their 
atmospheres  except  by  the  spectroscope.  Uranus  is  bright 
enough  so  that  its  spectrum  shows  10  broad  diffused 
bands,  between  C  and  F,  indicating  strong  absorption  by  a 
dense  atmosphere  very  different  from  that  of  the  earth, 
as  Keeler  has  shown.  The  position  of  these  lines  in  the 
red  is  sufficient  to  account  for  the  sea-green  tint  of  the 
planet.  Neptune's  color  is  almost  the  same  ;  and  its  spec- 
trum, if  not  so  faint,  would  probably  show  similar  absorp- 
tion bands. 

Surfaces  of  the  Planets 

Zodiacal  Light.  —  Interior  to  the  orbit  of  Mercury,  but 
possibly  stretching  out  beyond  the  path  of  the  earth,  is 
a  widely  diffused  disk  of  interplanetary  particles  moving 


The  Gegenschein 


UNIVERSITY 


round  the  sun,  mildly  reflecting  its  rays  to  us,  and  called 
the  zodiacal  light. 

The  illustration  shows  it  well  —  a  faintly  luminous  and  ill-defined 
triangular  area,  expanding  downward  along  the  ecliptic  toward  the 
western  horizon,  short- 
ly after  twilight  on 
clear,  moonless  nights 
from  January  to  April. 
Its  central  region  is 
brightest  and  slightly 
yellowish.  It  has  suf- 
fered no  change  for 
more  than  two  centu- 
ries. Its  spectrum  is 
short  and  continuous, 
without  bright  lines, 
though  possibly  a  few 
faint  dark  ones  are 
present.  In  tropic 
latitudes,  where  the 
ecliptic  always  stands 
high  above  the  hori- 
zon, the  zodiacal  light 
can  be  well  seen  in 
clear  skies  the  year 
round.  In  our  middle 
latitudes  it  cannot  be 
seen  early  in  autumn 
evenings,  because  of 
the  slight  inclination 
of  the  ecliptic  to  the 
horizon,  as  the  next 
figure  shows  :  that  part 

of  the  zodiacal  light  near  a  and  above  the  horizon,  ////,  is  lost  in 
low-lying  mist  and  haze.  In  autumn  it  must  be  looked  for  in  the  east 
just  before  dawn,  leaning  toward  the  right  in  our  latitudes. 

The  Gegenschein.  —  This  is  a  name  of  German  origin,  given  to  a 
zodiacal  counterglow  discovered  by  Brorsen  in  1854  —  an  exceedingly 
faint  and  evenly  diffused  nebulous  light,  nearly  opposite  the  sun,  some- 
times slightly  south  and  again  somewhat  north  of  the  ecliptic.  A 
bright  star  or  planet  near  by  is  sufficient  to  overmaster  its  light ;  even 
proximity  to  the  Milky  Way  obliterates  it.  Sometimes  the  gegenschein 


The  Zodiacal  Light  in  Tropic  Latitudes 


352 


The  Planets 


is  circular,  at  others  elliptic  ;  and  its  diameter  varies  between  3°  and  13°, 
according  to  Barnard  and  Douglass.     It  is  best  seen  in  September  and 

October,  in  Sagittarius 
and  Pisces.  No  satisfac- 
tory theory  as  to  its  cause 
exists.  Very  likely  the 
gegenschein  is  due  to 
clouds  of  small  inter- 
planetary bodies,  though 
possibly  it  may  be  caused 
by  abnormal  refraction  in 


Why  Zodiacal  Light  is  Invisible  in  our  Fall  Evenings 


our  atmosphere. 


Surface  of  Mercury.  —  Mercury  is  so  small  a  planet  and 
so  distant  from  the  earth  that  the  disk  is  disappointing. 
In  the  northern  hemi- 
sphere he  is  best  seen 
near  greatest  elongation 
east  in  spring,  and  great- 
est elongation  west  in 
autumn ;  because  he  is 
then  in  the  northernmost 
part  of  the  zodiac,  where 
meridian  altitude  is  as 
great  as  possible.  Mark- 
ings on  the  surface  of 
Mercury  are  described  by 
Lowell  as  less  difficult 
than  those  on  Venus ; 

without  color,  and  lines  rather  than  patches ;  and  the  fact 
that  they  do  not  change  from  hour  to  hour,  nor  per- 
ceptibly from  day  to  day,  shows  that  the  planet's  periods 
of  rotation  and  revolution  are  the  same.  Above  are  nine 
drawings  of  the  planet  in  October,  1896;  also  on  the  next 
page  Lowell's  chart  of  all  that  portion  of  the  surface  of 
Mercury  ever  visible,  amounting  to  five  eighths  of  the 
entire  spherical  superficies.  The  surface  is  probably  rough, 


Typical  Drawings  of  Mercury,   1896  i  Lowell) 


Surface  of  Venus 


353 


because,  like  the  moon,  the  amount  of  light  reflected 
from  a  unit  of  surface  increases  from  crescent  phase 
to  full. 

Illuminated  Hemisphere  of  Venus.  —  The  unillumined 
half  of  Venus  appears  to  be  forever  sealed  from  investiga- 
tion by  our  eyes ;  but 
that  part  of  the  sunward 
hemisphere  turned  to- 
ward us  has  been  repeat- 
edly drawn  during  the 
last  250  years.  Only  dull, 
indefinite  markings,  or 
spots  covering  large  areas 
have,  however,  been  seen 
until  recently.  The  illus- 
tration below  shows  the 
general  nature  of  mark- 
ings drawn  by  the  earlier  observers.  Frequently  the  ter- 
minator was  irregularly  curved,  indicating  mountains  of  great 


Chart  of  All  the  Visible  Surface  of  Mercury 
(Lowell) 


Venus  as  drawn  by  Mascari  in  1892 

height;  and  polar  caps  were  depicted.  According  to  recent 
observations  of  Lowell,  however,  the  disk  of  Venus  is  color- 
less, and  resembles  'simply  a  design  in  black  and  white 
over  which  is  drawn  a  brilliant  straw-colored  veil.'  This 
TODD'S  ASTRON.  —  23 


354 


The  Planets 


veil  is  doubtless  the  planet's  atmosphere.     No  polar  caps 
were  seen. 


Venus  as  drawn  by  Lowell  in   1896 


Markings  on  the  disk,  seen  and  drawn  independently  by  Lowell  and 
his  assistants,  Douglass,  See,  and  others,  are  broad  belts,  not  spots. 

Three  specimen  drawings  are 
adjacent.  The  markings  are 
mostly  great  circles  on  the 
planet's  surface,  and  many 
of  them  radiate  from  a  sin- 
gle center,  as  the  accom- 
panying chart  shows.  They 
partake  of  the  general  bril- 
liance of  the  disk,  and  their 
lack  of  contrast  renders  them  difficult  objects,  except  to  observers 
trained  in  visualizing  faint  planetary  detail.  Three  slight  protuber- 
ances, probably  mountains,  were  detected  on  the  terminator.  This 
interesting  work  of  the  Lowell  Observatory,  located  at  Flagstaff, 
Arizona,  was  done  in  the  latter  months  of  1896.  The  fine  atmos- 
pheric conditions  of  that  region,  and  the  critical  manner  in  which 
the  observations  were  made, 
lend  significance  to  the  fore- 
going results,  although  they 
are  not  as  yet  fully  confirmed 
by  observers  in  other  parts 
of  the  world.  Taken  in  con- 
nection with  the  practical  cer- 
tainty of  an  atmosphere,  the 
constant  aspect  of  one  hemi- 


sphere perpetually  toward  the 
sun  is  very  significant ;  prob- 
ably atmospheric  currents 
would  gradually  remove  all 
water  and  nearly  all  moisture 
from  the  sunward  hemi- 
sphere, and  deposit  it  as  ice 
on  the  dark  side  of  the 
planet.  This  affords  a  likely 

explanation  of  the  so-called  phosphorescence  of  the  dark  hemi- 
sphere; for  a  faint  light  diffused  over  the  unilluminated  portion  of 
the  disk  has  repeatedly  been  seen  by  many  good  observers. 

Surface  of  Mars  in  General.  —  Huygens,  in  1659,  made 
the  first  sketch  of  Mars  to  show  definite  markings ;  and  in 


Chart  of  Visible  Hemisphere  of  Venus  (Lowell) 


Surface  of  Mars 


355 


1840,  Beer  and  Maedler  drew  the  first  chart  of  the  planet. 
The  two  hemispheres  exhibit  a  marked  difference  in  bright- 
ness, the  northern  being  much  brighter.  Probably  it  is 
land,  while  the  southern  is  mainly  water;  but  in  general 
there  is  no  analogy  with  the  present  scattering  of  land 
and  water  on  the  earth.  Four  to  eleven  is  the  proportion 
here ;  but  on  Mars  land  somewhat 
predominates.  Probably  the  waters 
have  for  the  most  part  slight  depth. 
Extensive  regions  which  change  from 
yellow,  like  continents,  to  dark  brown, 
are  thought  to  be  marshes,  varying 
depth  of  water  causing  the  diversity 
of  color.  Mars  appears  to  be  so  far 
advanced  in  his  life  history  that  areas 
of  permanent  water  are  very  limited. 
The  border  of  the  disk  is  brighter 
than  the  interior,  and  changes  in  ap- 
parent brightness  of  certain  regions 
are  well  established.  In  consider- 
able part  these  depend  upon  the  an- 
gle of  vision  as  modified  by  axial 
turning  of  the  planet.  Photographs 
of  Mars  have  been  taken,  but  they 
show  only  salient  features  of  the  disk. 
Major,  a  well-known  region  (see  fifth  figure  on  page  358) 
appear  to  be  vegetation  rather  than  water.  Smoothness 
of  the  terminator,  along  which  a  few  projections  and 
flattenings  have  been  observed,  indicates  clearly  that  the 
Martian  surface  is  relatively  flat,  as  compared  with  the 
present  rugged  exterior  of  earth  and  moon. 

Orbits  of  Earth  and  Mars.  —  Inner  circle  in  next  illustration  rep- 
resents orbit  of  earth,  and  outer  one  orbit  of  Mars  eccentrically  placed 
in  true  proportion.  Around  inner  circle  are  indicated  positions  of  earth 


Mars  in  1877  (Green) 


Markings  of  Syrtis 


356 


The  Planets 


in  different  months,  and  around  outer  circle  are  shown  the  points  occu- 
pied by  Mars  at  opposition  time  in  the  several  years  indicated.  The 
most  favorable  opposition  of  Mars,  or  when  that  planet  is  at  the  mini- 
mum distance  of  35,000,000  miles  from  the  earth,  can  take  place  only 
in  August  and  September,  as  indicated  on  right-hand  side  of  diagram. 


Orbits  of  Mars  and  Earth,  showing  Least  and  Greatest  Distances  at  Opposition 

Similarly  on  left-hand  side  the  least  favorable  oppositions  occur  in  those 
years  when  the  opposition  time  falls  in  February  and  March.  Exact 
positions  of  Mars  at  recent  favorable  oppositions  are  shown  at  1877 
and  1892.  But  at  opposition,  October,  1894,  although  the  planet  was 
then  much  farther  from  earth,  still  he  culminated  higher  than  in  1892; 
because  the  sun  crosses  the  meridian  lower  in  October  than  in  August. 
Higher  northern  declination  enabled  the  planet  to  be  observed  to 
greater  advantage  in  1894  than  in  1892,  because  nearly  all  the  observa- 
tories of  the  world  are  located  in  its  northern  hemisphere.  Subsequent 


Polar  Caps  of  Mars 


357 


opposition  distances  of  Mars  are  all  unfav- 
orably great  until  1907  ;  or  better  still,  1909, 
which  will  occur  in  September,  in  nearly  the 
same  longitude  as  did  that  of  1877. 

Polar  Caps  of  Mars.  —  These  were 
discovered  by  Cassini  in  1666. 
Rather  more  than  a  century  later, 
Sir  William  Herschel  first  made  out 
their  variation  in  size  with  progress 
of  the  seasons  on  Mars,  which  are 
in  general  similar  to  ours,  although 
longer,  because  the  Arean  year  is 
longer.  Near  the  end  of  Martian 
winter  the  polar  caps  are  largest, 
and  they  gradually  shrink  in  size 
till  the  end  of  summer. 

This  remarkable  diminution  of  the  south 
polar  cap  has  been  repeatedly  observed  since 
Herschel's  time,  and  the  illustrations  show 
its  progress  during  the  Martian  spring  and 
summer  of  1894.  Without  much  doubt, 
this  shrinking  of  the  polar  cap  is  due 
to  melting  of  snow  and  ice.  The  north 
polar  cap  exhibits  a  like  succession  of  phe- 
nomena, though  much  more  difficult  to 
observe,  because  the  direction  of  the  planet's 
axis  in  space  is  such  that  when  this  pole  is 
turned  toward  us.  Mars  at  opposition  is 
nearly  twice  as  far  away  as  when  the 
south  pole  is  toward  us.  The  north  polar 
cap  covers  the  planet's  pole  of  rotation 
almost  exactly ;  but  the  center  of  the 
south  is  now  displaced  about  200  miles 
from  the  true  pole,  and  this  distance  varies 
irregularly  from  time  to  time.  At  the 
beginning  of  the  summer  season  of  1892, 
the  south  polar  cap  was  1200  miles  in  diam- 
eter; gradually  a  long,  dark  line  appeared 
near  the  middle,  and  eventually  cut  the  cap 
in  two;  the  edge  became  notched;  dark 


Shrinkage  and  Disappearance 
of  South  Polar  Cap  in  1894 
(Barnard  in  Popular  Astronomy] 


(It  Top  of  Fork  on  left  is  Fastigium  Aryn. 
Dark  Horn  nearly  central  is  Margantifer  Sinus 


(3^  Seven  Canals  diverge  from  Sinus  Tita 
num.   Eumenides  Orcusthreads  Nine  Oases 


(5)    Largest    Roundish    Area    is    Hellas. 
Below  Hellas  is  the  pointed  Syrtis  Major 


(2)    Soils      Lacus      is      nearly      central. 
Double  Nectar  runs  to  the  left  from  it 


<4*  The  Rectangle  is  Trivium  Charonti 
Dark  Mare  Cimmerium  is  central 


(6)  Among    Double   Canals    are    Euphrates 
(nearly  vertical),  and  Asopus  perpendicular  to  it 


Mars  according  to  Schiaparelli  and  Lowell  (1877-1894) 
358 


Canals  and  Oases  of  Mars  359 

spots  grew  in  its  central  regions,  and  isolated  patches  were  seen  to 
separate  from  the  principal  mass,  and  later  dissolve  and  disappear. 
The  phenomenon  was  similar  in  1894,  as  Barnard's  12  pictures  of 
the  cap  show  (page  357).  In  three  months  the  cap\s  diameter  had 
shrunk  to  170  miles,  and  in  eight  months  it  had  vanished  entirely  c 

Canals  and  Oases  of  Mars.  —  This  diminution  of  the  polar 
cap  seems  to  afford  a  key  to  the  physiographic  situa- 
tion on  Mars ;  for,  coincidently  with  its  shrinking,  a  strange 
system  of  markings  begins  to  develop,  traversing  continen- 
tal areas  in  all  directions,  and  forming  a  network  of  dark- 
ish narrow  lines. 

Six  engravings  opposite  exhibit  the  planet's  surface  in  all  longitudes, 
and  show  the  canals  much  intensified.  All  appear  on  the  Mat  disk  as 
either  straight  or  uniformly  curving  lines  ;  and  if  transferred  to  the  sur- 
face of  a  globe,  they  are  found  to  traverse  it  on  arcs  of  great  circles. 
Many  canals  connect  with  projections  of  bluish-green  regions,  which 
may  be  actual  gulfs  and  bays.  At  numerous  intersections  with  other 
canals  are  oval  or  circular  spots,  called  oases,  many  of  them  appearing 
like  hubs  from  which  canals  radiate  as  spokes.  Their  average  diameter  is 
about  130  miles.  For  example,  seven  canals  converge  to  Lacus  Phoenicis. 
The  most  signal  marking  of  this  character  is  in  Arean  latitude  about  30° 
south  (shown  above  middle  of  the  second  disk  opposite).  Though 
often  called  the  '  oculus,1  or  eye  of  Mars,  it  is  now  generally  known  as 
Solis  Lacus,  or  Lake  of  the  Sun.  Its  breadth  is  300  miles,  and  its  length 
540  miles.  Through  Solis  Lacus  run  narrow  double  canals,  whose 
length  is  much  less  than  the  average.  In  general  the  canals  average 
about  1200  miles ;  but  the  longest  one  is  Eumenides-Orcus,  whose  com- 
bined length  is  3500  miles,  or  nearly  equal  to  the  entire  diameter  of 
the  planet.  Length  enhances  their  visibility,  for  the  average  width  is 
only  about  30  miles.  Canals  were  first  discovered  by  Schiaparelli  in 
1877.  They  are  bluish-green  in  color,  and  have  been  repeatedly  ob- 
served by  their  discoverer  in  Italy ;  Lowell,  in  Arizona ;  Perrotin,  in 
France;  W.  H.Pickering,  in  South  America;  astronomers  of  the  Lick 
Observatory ;  Wilson,  in  Minnesota ;  and  Williams,  in  England.  About 
200  have  been  seen  in  all ;  so  that  their  reality  is  now  generally  con- 
ceded. But  a  steady  atmosphere  is  requisite  to  reveal  them. 

Doubling  of  the  Canals  and  Oases.  —  Lowell,  one  of  the  few  ob- 
servers who  have  yet  seen  the  doubling  of  the  canals,  thus  describes 
this  marvelous  phenomenon  :  — 

i  Upon  a  part  of  the  disk  where  up  to  that  time  a  single  canal  has 
been  visible,  of  a  sudden,  some  night,  in  place  of  the  single  canals,  are 


360  The  Planets 

perceived  twin  canals,  — as  like,  indeed,  as  twins,  if  not  more  so,  run- 
ning side  by  side  the  whole  length  of  the  original  canal,  usually  for 
upwards  of  a  thousand  miles,  of  the  same  size  throughout,  and  abso- 
lutely parallel  to  each  other.  The  pair  may  best  be  likened  to  the 
twin  rails  of  a  railroad  track.  The  regularity  of  the  thing  is  startling.' 

Many  double  canals  are  shown  in  the  sixth  figure  on  page  358.  Aver- 
age distance  between  the  twin  canals  is  150  to  200  miles.  This  phe- 
nomenon, still  a  mystery,  does  not  appear  to  be  an  effect  of  either 
optical  illusion  or  double  refraction ;  but  rather  a  really  double  exist- 
ence, seen  only  under  exceptionally  favorable  conditions  of  atmosphere. 
More  strangely  still,  the  oases  too  are  occasionally  seen  to  be  double. 

Meaning  of  Canal  and  Oasis.  —  It  is  the  design  of  physical  science 
not  only  to  record  but  to  explain  appearances ;  and  the  canals,  whether 
double  or  single,  have,  to  many  astronomers  who  have  seen  them,  a 
look  of  artificiality  rather  than  naturalness.  If  we  accept  the  former, 
the  explanation  of  the  canals  themselves,  advanced  by  W.  H.  Pickering 
and  reinforced  by  the  argument  of  Lowell,  seems  very  plausible : 
water  is  scarce  on  the  planet ;  with  melting  of  the  polar  caps,  it  is  grad- 
ually conducted  along  narrow  channels  through  the  middle  of  the 
canals,  thereby  irrigating  areas  of  great  breadth  which,  with  the  ad- 
vance of  the  season,  become  clothed  with  vegetation.  Similarly  the 
oases ;  and  at  our  great  distance,  it  is  vegetation  which,  although  invis- 
ible in  the  Arean  winter,  grows  visible  as  canal  and  oasis  with  every 
return  of  spring.  The  fact  that  oases  are  seen  only  at  junctions  of 
canals,  and  not  elsewhere,  greatly  strengthens  this  argument.  Of 
course,  acceptance  of  this  theory  implies  that  Mars  in  ages  past,  has 
been,  and  may  be  still,  peopled  by  intelligent  beings  ;  and  that  continu- 
ation of  their  existence  upon  that  planet,  during  secular  dissipation  of 
natural  water  supply,  has  rendered  extensive  irrigation  a  prime  requisite. 
For  animal  life,  of  types  known  to  us,  is  dependent  upon  vegetable  life ; 
which,  in  turn  is  conditional  upon  water  distribution,  either  natural  or 
artificial.  But  only  by  long  continued  observation  of  the  behavior  of 
canal  and  oasis  in  both  hemispheres  of  Mars,  can  we  hope  for  a  rational 
solution  of  the  question  of  life  in  another  world  than  ours.  Such 
difficult  research  Lowell  and  his  able  corps  of  observers  are  now  faith- 
fully prosecuting  with  a  24-inch  Clark  telescope  in  favorable  skies. 

Seasonal  Changes.  —  Striking  seasonal  changes  seen  to 
keep  step  with  progress  of  Mars  in  his  orbit,  are  best  ex- 
hibited by  direct  comparison  between  drawings  at  intervals 
of  several  months.  Three  such  are  chosen  in  plate  vi.  The 
region  known  as  Hesperia  is  central  in  all.  The  first,  7th 


f 

a 


£> 


Discoveries  of  Small  Planets  361 

June,  1894,  corresponds  to  early  spring  on  Mars.  South 
polar  snows  have  just  begun  to  melt.  Everywhere  encir- 
cling it  is  the  dark  area,  as  if  water  from  the  melting  of  the 
cap;  for  this  band  follows  the  cap  as  it  shrinks,  becom- 
ing less  in  width  as  the  cap  grows  smaller.  This  is  shown 
in  the  middle  disk,  which  corresponds  to  early  summer. 
Mark  the  other  changes  in  the  disk :  (i)  the  general  thin- 
ning out  of  dark  areas  which  on  the  actual  planet  are 
greenish-blue ;  (2)  the  increase  in  intensity  of  reddish 
ochre  regions  through  the  southern  hemisphere,  as  if  the 
water  had  in  considerable  part  evaporated,  Hesperia 
already  beginning  to  show  as  an  obliaAiie,  V-shaped,  red- 
dish marking  in  the  center  of  the  disk;  (3)  progress  in 
development  of  canals,  though  not  as  yet  far  advanced. 
As  the  planet  approaches  late  summer,  in  the  third  draw- 
ing, Hesperia  has  become  a  broad  cleft  through  the  water 
area,  three  canals  are  particularly  well  developed  in  the 
northern  hemisphere,  and  the  south  polar  cap  has  practi- 
cally vanished.  In  other  longitudes  like  changes  went  on 
simultaneously,  and  in  the  same  significant  and  seemingly 
obvious  direction. 

Discoveries  of  Small  Planets.  —  In  1800,  the  closing  year 
of  the  eighteenth  century,  conspicuous  absence  of  a  planet 
between  Mars  and  Jupiter  as  required  by  Bode's  law,  led  to 
an  association  of  24  astronomers  intent  upon  search  for 
the  missing  body.  Piazzi-of  Sicily  inaugurated  the  long 
list  of  discoveries  by  finding  the  first  one  on  the  first  night 
of  the  1 9th  century  (ist  January,  1801).  He  called  it 
Ceres,  that  being  the  name  of  the  tutelary  divinity  of 
Sicily.  Three  others,  named  Pallas,  Juno,  and  Vesta, 
were  found  by  1807,  but  the  fifth  was  not  discovered  till 
1845. 

Since  1847  no  year  has  failed  to  add  at  least  one  to  the  number,  and 
in  1896  the  increase  was  40.  The  total  number  is  now  approaching 


362  The  Planets 

500.  Of  these,  75  were  discovered  in  the  United  States,  mainly  by  Peters 
(48)  at  Clinton,  New  York,  and  Watson  (22)  at  Ann  Arbor,  Michigan. 
Palisa,  of  Vienna,  found  no  less  than  72.  In  1891,  Wolf  of  Heidelberg 
inaugurated  discoveries  of  these  bodies  by  the  aid  of  photography, 
and  he  has  discovered  about  60  in  this  manner :  a  sensitive  plate  ex- 
posed for  two  or  three  hours  to  a  suspected  region  of  sky  makes  a  per- 
manent record  of  all  the  stars  as  round  disks,  and  of  any  small  planets 
as  short  trails  because  of  their  apparent  motion  during  exposure.  So 
they  are  discovered  about  2O-fold  more  readily  than  by  the  old-fash- 
ioned method  at  the  eyepiece  of  a  telescope.  Charlois  of  Nice  has 
found  nearly  90  small  planets  by  photography.  About  100  of  the  more 
recent  discoveries  are  yet  without  names,  and  are  designated  by  their 
number,  thus  (asp  ;  also  by  a  double  letter  and  year  of  discovery,  as 
1897  DE  =  (428).  Probably  there  are  hundreds  more,  and  possibly  thou- 
sands. Discoveries  are  disseminated  by  Ritchie's  international  code. 

Orbits  and  Origin  of  Small  Planets.  —  The  orbits  of 
small  planets,  although  linked  together  inseparably,  still 
present  wide  degrees  of  divergence.  They  are  by  no 
means  evenly  distributed :  in  those  regions  of  the  zone 
where  a  simple  relation  of  commensurability  exists  between 
the  appropriate  period  of  revolution  and  the  periodic  time 
of  Jupiter,  gaps  are  found,  resembling  those  shown  farther 
on  as  existing  in  the  ring  of  Saturn. 

Especially  is  this  true  for  distances  corresponding  to  one  half  and  one 
third  of  Jupiter's  period.  Not  only  are  the  orbits  of  small  planets  far 
from  concentric,  but  they  are  inclined  at  exceptionally  large  angles  to  the 
ecliptic,  that  of  Pallas  (2)  being  35°.  Several  groups  exist  having  a 
near  identity  of  orbits,  one  such  group  including  1 1  members.  Poly- 
hymnia (sT)  is  much  perturbed  by  the  attraction  of  Jupiter,  and  its  mo- 
tion has  recently  been  employed  by  Newcomb  in  finding  anew  the  mass 
of  the  giant  planet,  equal  to  1(H*  ^  that  of  the  sun.  Victoria  (12),  Sappho 
(*j),  and  others,  on  account  of  favorable  approach  to  the  earth,  have  been 
very  serviceable  in  the  hands  of  Gill  and  Elkin  in  helping  to  ascertain 
sun's  distance  from  earth.  Data  concerning  orbits  of  these  bodies  are 
published  each  year  in  the  Berliner  Astronomi sches  Jahrbuch. 

Olbers  early  originated  the  theory,  now  disproved,  that 
small  planets  had  their  origin  in  explosion  of  a  single 
great  planet.  Most  probably,  however,  proximity  of  so 


The  Surface  of  Jupiter 


363 


massive  a  planet  as  Jupiter 
is  responsible  for  the  exist- 
ence of  a  multitude  of  small 
bodies  in  lieu  of  one  larger 
one ;  for  his  gravitative  action 
upon  the  ring  in  its  early 
formative  stage,  in  accord- 
ance with  principles  of  the 
evolution  of  planets  may 
readily  have  precluded  ulti- 
mate condensation  of  the 
ring  into  a  separate  planet. 
Surface  of  Jupiter.  —  In  a 
telescope  of  even  moderate 
size,  Jupiter  appears,  as  in 
this  typical  view,  striped  with 
many  light  and  dark  belts, 
of  varying  colors  and  widths, 
lying  across  the  disk  parallel 
to  each  other  and  to  his  equa- 
tor, or  nearly  so.  They  al- 
ways appear  practically 
straight  because  the  plane 
of  Jupiter's  equator  always 
passes  very  nearly  through 
the  earth.  The  belts  are  not 
difficult  to  see ;  but  the  tele- 
scope had  been  invented  20 
years  before  they  were  dis- 
covered, at  Rome,  in  1630. 
Usually  the  equatorial  zone, 
about  25°  broad,  is  lightest  in 
hue,  and  almost  centrally 
through  it  runs  a  very  narrow 


Jupiter  in  1889  (Keeler) 


364 


The  Planets 


dark  stripe.  Larger  telescopes  reveal  a  variety  of  spots 
and  streaks  in  this  zone,  and  permanence  of  markings  is 
rather  the  exception  than  the  rule.  It  appears  to  be  a 
region  of  great  physical  commotion.  Bordering  this  zone, 
on  either  side,  are  usually  two  broad  reddish  belts,  about 
20°  of  latitude  in  width.  These  are  zones  of  little  dis- 
turbance, but  the  southern  one  often  appears  divided. 

Just  beyond  it  is  the  '  great 
red  spot.'  Here  and  there 
white  cloudlike  masses,  near 
the  edge  of  the  equatorial 
zone,  appear  to  flow  over  into 
the  red  belts  as  long  oblique 
streamers,  seemingly  dividing 
these  broad  zones  into  two  or 
three  narrow  stripes.  Farther 
from  the  equator  are  still  other 
belts,  growing  narrower  as  the 
poles  are  approached,  because 
curvature  of  the  spherical  sur- 
face foreshortens  them ;  and 
all  around  the  limb,  whether 
at  poles  or  equator,  the  belts 
fade  into  indistinctness.  Color 
Jupiter's  Great  Red  Spot  in  1881  and  an(j  intensity  of  the  principal 

1885  (Denning)  * 

belts  are  by  no  means  con- 
stant, their  hue  being  at  times  brownish,  copper-colored, 
and  purple.  Of  the  two  hemispheres,  the  reddish  tint  of 
the  southern  is  rather  more  pronounced. 

Jupiter's  Great  Red  Spot.  —  Probably  this  gigantic  mark- 
ing, whose  area  exceeds  that  of  our  whole  earth,  has  long 
been  forming ;  for  although  it  was  not  certainly  seen  until 
1869,  and  still  more  definitely  in  1878  first  by  Pritchett,  there 
are  indications  that  Cassini,  at  Paris,  observed  it  in  1685. 


A   Chart  of  Jupiter 


365 


The  opposite  illustrations  show  its  appearance  in  1881  and  1885. 
Breadth  of  this  elliptic  marking  was  about  8000  miles,  and  length  30,000. 
The  great  red  spot  has  not  been  uniformly  conspicuous,  for  it  nearly 
faded  out  in  1883-84.  The  year  following  a  white  cloud  appeared  to 
cover  the  middle,  making  it  look  like  a  chain-link.  The  lowest  drawing 
(page  363)  shows  its  appearance  in  1889.  Now  quite  invisible,  it  may 
have  a  periodicity,  and  again  reappear.  Cloud  markings  near  it  have 
been  observed  to  be  strikingly  repelled.  If  the  spot  remained  station- 
ary upon  the  planet's  surface,  it  might  be  simply  a  vast  fissure  in  the 
outer  atmospheric  envelope  of  Jupiter,  through  which  are  seen  dense 
red  vapors  of  interior  strata,  if  not  the  planet's  true  surface ;  but  its 
slow  drift  precludes  this  theory.  No  satisfactory  explanation  of  the 
great  red  spot  has  yet  been  advanced. 

A  Chart  of  Jupiter. — Notwithstanding  considerable  variations  in 
detailed  appearance  of  Jupiter's  disk,  many  larger  markings  present  a 

S 


240 


270  300  330  0  30  60 

Approximate  Chart  of  a  Portion  of  Jupiter  in  1895  (Henderson) 


sufficient  permanence  from  month  to  month  to  admit  of  charting. 
Adjacent  is  such  a  chart,  on  the  Mercator  projection,  and  intended 
to  be  accurate  as  to  general  features  only.  Center  of  the  great  red 
spot  is  taken  as  origin  of  longitudes.  The  principal  belts  and  the  more 
important  white  spots  are  clearly  indicated.  From  the  construction 
of  many  such  charts,  at  intervals  of  about  a  year,  much  can  be  learned 
about  the  planet's  atmosphere,  present  physical  condition,  and  future 
development.  As  yet  photography,  successfully  applied  by  Common, 
and  Russell,  and  at  the  Lick  Observatory,  although  showing  accurately 
a  great  quantity  of  detail,  including  a  multitude  of  white  and  dark  spots, 
does  not  equal  the  eye  in  recording  finer  markings.  Length  of  expo- 
sure and  unsteadiness  of  atmosphere  are  the  chief  obstacles.  Hough 


366  The  Planets 

in  America  and  Williams  in  England  have  been  constant  students  of 
Jupiter. 

Surface  of  Saturn.  —  A  telescope  of  only  two  inches' 
aperture  will  show  the  ring  of  Saturn,  also  Titan,  his  larg- 
est satellite.  A  four-inch  object  glass  will  reveal  four  other 
satellites  on  favorable  occasions.  The  entire  disk  appears 
as  if  enveloped  in  a  thin,  faint,  yellowish  veil.  At  irregular 


Saturn  and  his  Rings  (drawn  by  Pratt  in  1884) 

intervals  belts  are  seen  similar  to  Jupiter's  ;  but  they  do  not 
persist  so  long,  and  are  much  fainter.  As  a  rule  Saturn's 
equatorial  belt  is  his  brightest  region,  and  an  olive-green 
zone  often  caps  the  pole.  Excellent  photographs  have 
been  taken  at  the  Lick  and  Greenwich  Observatories. 

At  intervals  of  nearly  1 5  years,  the  belts  appear  very  much  curved,  as  in 
the  illustration  above ;  because  the  earth  is  then  about  26°  above  or 
below  the  plane  of  the  planet's  equator,  this  being  the  angle  by  which 
the  axis  of  Saturn  is  inclined  to  a  perpendicular  to  its  orbit  plane.  Mid- 
way between  these  epochs,  the  belts  appear  practically  curveless,  like 
Jupiter's,  because  the  plane  of  Saturn's  equator  is  then  passing  near  the 
earth  (see  drawing  opposite  on  the  right).  Few  bright  spots  and 


Saturn  s  Rings  and  their  Phases          367 

irregularities  of  marking  characterize  this  planet,  and  his  true  period  of 
rotation  is  on  that  account  difficult  to  ascertain.  Celestial  photography 
is  not  yet  sufficiently  perfected  to  afford  much  assistance  in  recording 
the  minute  details  of  so  small  a  disk  as  Saturn's.  With  the  invention 
of  more  highly  sensitive  plates,  requiring  a  much  shorter  exposure, 
unavoidable  blurring  of  atmosphere  will  be  less  harmful.  Numerous 
faint  and  nearly  circular  dark  and  white  spots  or  mottlings  were 
observed  on  the  ball  in  1896. 

Saturn's  Rings  and  their  Phases.  —  Saturn  is  surrounded 
by  a  series  of  thin,  circular  plane  rings  which  generally 


Very  Early  Drawings  of  Saturn 
(in  the  1  7th  Century) 


Saturn  in   1891.    (Mark  the  Excess- 
ive Polar  Flattening) 


appear  elliptical  in  form.  To  astronomers  of  the  first  half 
of  the  i  /th  century,  Saturn  afforded  much  puzzlement, 
and  they  drew  the  planet  in  a  variety  of  fanciful  forms, 
some  of  which  are  here  shown.  Huygens  first  guessed 
the  riddle  of  the  rings  in  1655.  When  widely  open, 
as  in  1884  (opposite  page),  and  in  1898  and  1899,  a  keen- 
eyed  observer,  even  with  a  small  telescope,  can  see  faint, 
darkish  lines  or  markings  near  the  middle  of  the  ring. 
These  are  divisions  of  the  system,  and  there  are  three 
complete  rings;  (A)  outer  bright  ring,  (j5)  inner  bright 
ring,  (C)  innermost  or  crape  ring. 


368 


The  Planets 


1878 


1882 


1885 


1889 


1891 


1893 


1895 


1897 


1899 


1901 


1903 


1905 


1907 


Phases  of  the 
Ring  of  Saturn 


While  Saturn  moves  round  the  sun,  the  ring  main- 
tains its  own  plane  constant  in  direction,  just  as  earth's 
equator  remains  parallel  to  itself.  Consequently  the 
plane  of  Saturn's  rings  sometimes  passes  through  the 
earth,  sometimes  through  the  sun,  and  again  between 
earth  and  sun.  At  these  times  the  rings  of  Saturn 
actually  disappear  from  view,  or  nearly  so,  as  just 
illustrated.  In  the  first  case,  the  ring  is  so  thin  that 
it  cannot  be  seen  when  the  earth  is  exactly  in  the 
plane  of  it.  In  the  second,  the  ring  disappears  be- 
cause the  sun  is  shining  on  neither  side  of  it,  but 
only  on  its  edge.  The  ring  may  disappear  in  the 
third  instance  when  earth  and  sun  are  on  opposite 
sides  of  it,  and  therefore  only  the  unillumined  face  of 
the  ring  is  turned  toward  us.  Disappearances  due  to 
these  causes  take  place  about  every  15  years,  or  one 
half  the  periodic  time  of  Saturn,  the  next  occurring 
in  1907,  as  the  adjacent  figures  (for  inverting  tele- 
scopes) show.  Intervals  between  disappearances  are 
unequal  partly  because  of  eccentricity  of  Saturn's  or- 
bit, perihelion  occurring  in  1885  and  aphelion  in  1899. 

Size  and  Constitution  of  the  Rings.  —  The 
dimensions  of  the  ring  system  are  enor- 
mous, especially  in  comparison  with  its 
thickness,  which  cannot  exceed  100  miles. 
Seen  edge  on,  it  has  the  appearance  of  a 
fine  and  often  broken  hair  line  (page  367). 

Outer  diameter  of  outside  ring  is  173,000  miles, 
and  its  breadth,  11,500  miles.  Then  comes  the 
division  between  the  two  luminous  rings,  discovered 
by  Cassini  in  1676:  its  breadth  is  2400  miles.  Outer 
diameter  of  inner  bright  ring  is  145,000  miles,  and  its 
breadth,  17,500  miles.  Next,  the  innermost  or  dusky 
ring,  discovered  by  Bond  in  1850 :  its  inner  diameter 
is  90,000  miles,  and  its  breadth  10,000  miles ;  and  it 
joins  on  the  inner  bright  ring  without  any  apparent 
division.  So  gauzy  is  it  that  the  ball  of  Saturn  can 
be  seen  directly  through  it,  except  at  the  outer  edge. 
Characteristic  of  the  inner  bright  ring  is  a  thickening 
of  its  outer  edge,  —  much  the  brightest  zone  of  the 
ring  system.  The  rings  of  Saturn  are  neither  solid 


The  Discovery  of  Neptune  369 

nor  liquid,  but  are  composed  of  enormous  clouds  or  shoals  of  very  small 
bodies,  possibly  meteoric,  traveling  round  the  planet,  each  in  an  orbit 
of  its  own,  as  if  a  satellite.  Perhaps  they  are  thousands  of  miles  apart 
in  space ;  but  so  distant  is  the  planet  from  the  earth  and  so  numerous 
are  the  particles  that  they  present  the  appearance  of  a  continuous  solid 
ring.  Keeler  has  demonstrated  by  the  spectroscope  this  theory  of  the 
constitution  of  Saturn's  rings,  showing  that  inner  particles  move  round 
the  primary  more  swiftly  than  outer  ones  do,  in  accord  with  Kepler's 
third  law.  The  periodic  time  of  innermost  particles  is  5  h.  50  m.,  or 
but  little  more  than  half  the  rotation  time  of  the  ball  itself,  which, 
according  to  some  observers,  is  slightly  displaced  from  the  center  of 
the  rings.  Not  impossibly  the  ring  system  is  a  transient  feature,  and 
may  be  a  ninth  satellite  in  process  of  formation  (page  467) . 

Surface  of  Uranus  and  Neptune.  —  The  great  planet 
Uranus,  the  first  one  ever  found  with  the  telescope,  was 
discovered  by  Sir  William  Herschel,  I3th  March,  1781. 
Calculation  backward  showed  that  this  planet  had  been 
observed  about  20  times  during  the  century  preceding, 
and  mistaken  for  a  fixed  star.  So  remote  is  Uranus  and 
so  small  the  apparent  disk  that  very  few  observers  have 
been  able  to  detect  anything  whatever  on  his  pale  green 
surface.  Some  have  seen  belts  resembling  those  on 
Jupiter,  others  a  white  spot  from  which  a  rotation  period 
equal  to  10  hours  was  found.  More  recently  the  planet 
has  been  sketched  by  Brenner,  from  the  clear  skies  of 
Istria,  and  six  of  his  drawings  are  reproduced  on  the  next 
page.  The  markings  appear  neither  numerous  nor  defi- 
nite. If  so  little  is  found  upon  Uranus,  vastly  less  must 
be  expected  from  Neptune,  and  no  marking  whatever  has 
yet  been  certainly  glimpsed. 

The  Discovery  of  Neptune.  —  The  discovery  of  Neptune 
was  a  double  one.  Early  in  the  present  century  it  was 
found  that  Uranus  was  straying  widely  from  his  theoretic 
positions,  and  the  cause  of  this  deviation  was  for  a  long 
time  unsuspected.  Two  young  astronomers,  Adams  in  Eng- 
land, and  Le  Verrier  in  France,  the  former  in  1 843  and  the 
TODD'S  ASTRON.  —  24 


370  The  Planets 

latter  in  1845,  undertook  to  find  out  the  cause  of  this 
perturbation,  on  the  supposition  of  an  undiscovered  planet 
beyond  Uranus.  Adams  reached  his  result  first,  and 

English  astronomers  be- 
gan to  search  for  the 
suspected  planet  with 
their  telescopes,  by  first 
making  a  careful  map 
of  all  the  stars  in  that 
part  of  the  sky.  But 
Le  Verrier,  on  reaching 
the  conclusion  of  his 
search,  sent  his  result 

to  the  Berlin  observatory,  where  it  chanced  that  an  accurate 
map  had  just  been  formed  of  all  stars  in  the  suspected 
region.  On  comparing  this  with  the  sky,  the  new  planet, 
afterward  called  Neptune,  was  at  once  discovered,  23d 
September,  1846.  It  was  soon  found  that  Neptune,  too, 
had  been  seen  several  times  during  the  previous  half  cen- 
tury, and  recorded  as  a  fixed  star.  The  tiny  disk,  how- 
ever, is  readily  distinguishable  from  the  stars  around  it,  if  a 
magnifying  power  of  at  least  200  diameters  can  be  used. 
There  are  theoretic  reasons  for  suspecting  the  existence  of 
two  planets  exterior  to  Neptune ;  but  no  such  bodies  have 
yet  been  discovered,  although  search  for  them  has  been 
conducted  both  optically  and  by  means  of  photography. 


CHAPTER   XIV 

THE  ARGUMENT   FOR   UNIVERSAL   GRAVITATION 

SO    striking    a    confirmation    of     Newton's    law    was 
afforded  by  the  discovery  of  Neptune,  and  so  com- 
pletely does  the  universality  of  that  law  account  for 
the  motions  of  the  heavenly  bodies,  and  the  variety  of  their 
physical  phenomena,  that  the  present  chapter  is  devoted 
to  a  partial  outline  sketch  of  the  argument  for  universal 
gravitation. 

From  Kepler  to  Newton.  —  The  great  progress  made  by 
Kepler  in  dealing  with  the  motions  of  the  planets  had  not 
in  any  proper  sense  explained  those  motions  ;  for  his  three 
famous  laws  merely  state  how  the  planets  move,  without 
at  all  touching  the  reason  why  these  laws  of  their  motion 
are  true.  Before  this  question  could  be  answered,  the 
fundamental  principles  of  physics,  or  natural  philosophy 
as  it  was  called  in  his  day,  had  to  be  more  fully  under- 
stood. These  principles  concern  the  state  of  bodies  at 
rest  and  in  motion.  Meaning  of  the  term  rest  is  relative, 
and  absolute  rest  is  undefinable.  Motion  is  a  change  of 
place ;  and  absolute  rest  is  a  state  of  absence  of  motion. 
Galileo  early  in  the  i/th  century  was  the  first  philosopher 
who  ascertained  the  laws  of  motion  and  wrote  them  down. 
But  as  they  were  better  formulated  by  Newton,  his  name 
is  always  attached  to  them.  They  are  axioms,  an  axiom 
being  a  proposition  whose  truth  is  at  once  acknowledged 
by  everybody,  as  soon  as  terms  expressing  it  are  clearly 
understood.  Newton,  indeed,  in  his  great  work  entitled 


372  Argument  for  Gravitation 

the  Principia,  or  principles  of  natural  philosophy,  called 
these  laws  Axiomata,  sive  Leges  Motiis.  Antecedent  to 
proper  conception  of  Newton's  law  of  universal  gravitation 
must  come  an  understanding  of  the  three  fundamental 
laws  of  motion. 

Newton's  First  Law  of  Motion.  — The  first  law  reads  as 
follows :  Every  body  continues  in  its  state  of  rest  or  of 
uniform  motion  in  a  straight  line,  except  in  so  far  as  it 
may  be  compelled  by  force  to  change  that  state.  Newton 
asserts  in  this  law  the  physical  truth  that  a  state  of  uni- 
form motion  is  just  as  natural  as  a  state  of  rest.  To  one 
who  has  never  thought  about  such  things,  this  is  at  first 
very  difficult  to  realize ;  because  rest  seems  the  natural 
state,  and  motion  an  enforced  one.  But  difficulty  is  at 
once  dispelled,  as  soon  as  one  begins  to  inquire  into  the 
causes  that  stop  any  body  artificially  set  in  motion. 

A  baseball  rolling  upon  a  level  field  soon  stops  because,  in  moving 
forward,  it  must  repeatedly  rise  against  the  attraction  of  gravity,  in 
order  to  pass  over  minor  obstacles,  as  grass  and  pebbles.  Also  there 
is  much  surface  friction.  A  rifle  shot  soon  stops  because  resistance  of 
the  air  continually  lessens  its  speed,  and  finally  gravity  draws  it  down 
upon  the  earth.  A  vigorous  winter  game  common  in  Scotland  is  called 
curling.  The  curling  stone  is  a  smooth,  heavy  stone,  shaped  like  a 
much-flattened  orange,  and  with  a  bent  handle  on  top.  When  curling 
stones  are  sent  sliding  on  smooth  ice  as  swiftly  as  possible,  they  go  for 
long  distances  with  but  slight  reduction  of  speed,  thus  affording  an 
excellent  approximation  to  Newton's  first  law.  But  a  perfect  illustra- 
tion is  not  possible  here  on  the  earth.  If  it  were  practicable  to  project 
a  rifle  shot  into  space  very  remote  from  the  solar  system,  it  would  travel 
in  a  straight  path  for  indefinite  ages,  because  no  atmosphere  would 
resist  its  progress,  and  there  is  no  known  celestial  body  whose  attrac- 
tion would  draw  it  from  that  path. 

Newton's  Second  Law  of  Motion.  —  The  second  law 
reads :  Change  of  motion  is  proportional  to  force  applied, 
and  takes  place  in  the  direction  of  the  straight  line  in 
which  the  force  acts. 


Newton  s  Laws  of  Motion 


373 


This  law  is  easy  to  illustrate  without  any  apparatus.  Throw  a  stone 
or  other  object  horizontally.  Everybody  knows  that  its  path  speedily 
begins  to  curve  downward,  and  it  falls  to  the  ground.  From  the 
smooth  and  level  top  of  a  table  or  shelf,  brush  a  coin  or  other  small 
object  off  swiftly  with  one  hand  :  it  will  fall  freely  to  the  floor  a  few 


Illustrating  Newton's  Second  Law  of  Motion 

feet  away.  Repeat  until  you  find  the  strength  of  impulse  necessary 
to  send  it  a  distance  of  about  two  feet,  then  four,  then  six  feet,  as  in 
the  picture.  With  the  other  hand,  practice  dropping  a  coin  from  the 
level  of  the  table,  so  that  it  will  not  turn  in  falling,  but  will  remain 
nearly  horizontal  till  it  strikes  the  floor.  Now  try  these  experiments 
with  both  hands  together,  and  at  the  same  time,  Repeat  until  one 
coin  is  released  from  the  fingers  at  the  exact  instant  the  other  is 
brushed  off  the  table.  Then  you  will  find  that  both  reach  the  floor  at 
precisely  the  same  time ;  and  this  will  be  true,  whether  the  first  coin  is 
projected  to  a  distance  of  two  feet,  four  feet,  six  feet,  or  whatever  the 
distance.  Had  gravity  not  been  acting,  the  first  coin  would  have 
traveled  horizontally  on  a  level  with  the  desk,  and  would  have  reached 
a  distance  of  two  feet,  or  four  feet,  proportioned  to  the  impulse.  What 
the  second  law  of  motion  asserts  is  this :  that  the  constant  force  (grav- 
ity in  this  case)  pulls  the  first  coin  just  as  far  from  the  place  it  would 
have  reached,  had  gravity  not  been  acting,  as  the  same  force,  acting 


374  Argument  for  Gravitation 

vertically  and  alone,  would  in  an  equal  time  draw  it  from  the  state  of 
rest.  Whatever  distance  the  coin  is  projected,  the  '  change  of  motion ' 
is  always  the  vertical  distance  between  the  level  of  table  and  floor, 
that  is,  'in  the  direction  of  the  straight  line  in  which  the  force  acts.' 
The  law  holds  good  just  the  same,  if  the  coin  is  not  projected  hori- 
zontally, provided  the  floor  (or  whatever  the  coin  falls  on)  is  parallel 
to  the  surface  from  which  it  is  projected. 

Newton's  Third  Law  of  Motion.  — The  third  law  reads  : 
To  every  action  there  is  always  an  equal  and  contrary 
reaction  ;  or  the  mutual  actions  of  any  two  bodies  are 
always  equal  and  oppositely  directed.  This  law  com- 
pletes the  steps  necessary  for  an  introduction  to  the  single 
law  of  universal  gravitation,  because  it  deals  with  mutual 
actions  between  two  bodies,  or  among  a  system  of  bodies, 
such  as  we  see  the  solar  system  actually  to  be. 

To  illustrate  in  Newton's  own  words :  *  If  you  press  a  stone  with 
your  finger,  the  finger  is  also  pressed  by  the  stone.  And  if  a  horse 
draws  a  stone  tied  to  a  rope,  the  horse  (if  I  may  so  say)  will  be  equally 
drawn  back  toward  the  stone ;  for  the  stretched  rope,  in  one  and  the 
same  endeavor  to  relax  or  unstretch  itselt,  draws  the  horse  as  much 
toward  the  stone  as  it  draws  the  stone  toward,  the  horse.'  Action  and 
reaction  are  always  equal  and  opposite. 

So  when  one  body  attracts  another  from  a  distance,  the 
second  body  attracts  with  an  equal  force,  but  oppositely 
directed.  If  there  were  two  equal,  and  therefore  bal- 
anced, forces  acting  on  but  one  body,  that  would  be  in  equi- 
librium ;  but  the  two  forces  specified  in  this  third  law  act 
on  two  different  bodies,  neither  of  which  is  in  equilibrium. 
Always  there  are  two  bodies  and  two  forces  acting,  and 
one  force  acts  on  each  body.  To  have  a  single  force  is 
impossible.  There  must  be,  and  always  is,  a  pair  of 
forces  equal  and  opposite.  Horse  and  stone  advance  as  a 
unit,  because  the  muscular  power  of  the  horse  exerted 
upon  the  ground  exceeds  the  resistance  of  the  stone. 

Transition  to  the  Law  of  Gravitation. — Having  clearly 


New  tons  Law  of  Gravitation  375 

apprehended  the  meaning  of  Newton's  three  laws  of 
motion,  transition  to  his  law  of  universal  gravitation  is 
easy.  The  laws  of  motion,  however,  must  not  now  be 
thought  of  separately,  but  all  as  applying  together  and  at  the 
same  time.  First,  consider  the  earth  in  its  orbit.  Our  globe 
has  a  certain  velocity  as  it  goes  round  the  sun ;  it  would 
go  on  forever  in  space  in  a  straight  line,  with  that  same 
velocity,  except  that  some  deflecting  force  draws  it  away 
from  that  line.  This  change  of  motion  or  direction  from  a 
straight  line  must  be  proportional  to  the  force  producing  it, 
and  the  change  itself  must  indicate  direction  in  which 
the  force  acts ;  also,  if  there  is  a  force  acting  from  the  sun 
upon  the  earth,  there  must  be  an  equal  and  oppositely 
directed  force  from  the  earth  upon  the  sun,  for  action  and 
reaction  are  equal. 

Similarly  the  motion  of  other  planets  round  the  sun  ;  and 
Newton's  reasoning  and  mathematical  calculations,  based 
on  the  laws  of  Kepler,  made  it  perfectly  clear  that  planet- 
ary motions  might  be  dependent  upon  a  central  force 
directed  toward  the  sun,  the  intensity  of  this  force  grow- 
ing less  and  less  in  exact  proportion  as  the  square  of  the 
planet's  distance  grows  greater  :  thus  at  twice  the  distance 
the  intensity  is  but  one  fourth  as  great.  By  making  this 
single  hypothesis,  the  meaning  of  all  three  laws  of  Kepler 
was  perfectly  apparent.  But  could  the  action  of  any  such 
force  be  proved  ?  If  it  could,  the  motions  of  all  the  satel- 
lites round  their  primaries  might  be  accounted  for  by  sup- 
posing a  like  force  emanating  from  the  central  planets. 
This  would  mean,  too,  that  the  moon  must  move  round  us 
obedient  to  a  force  directed  toward  the  earth,  but  decreas- 
ing in  intensity  just  as  rapidly  as  square  of  moon's  distance 
from  our  center  increases.  Can  it  be  that  the  common 
attraction  of  gravity  which  draws  stones  and  apples  down- 
ward is  a  force  answering  to  this  description  ?  Why 


376  Argument  for  Gravitation 

should  it  attract  only  common  objects  near  at  hand  ? 
Why  may  not  the  realm  of  this  mysterious  force  extend 
to  the  moon  ?  To  the  calculation  of  this  problem,  New- 
ton next  addressed  himself. 

Gravitation  holds  the  Moon  in  her  Orbit.  —  If  gravity 
causes  the  apple  to  fall  from  the  tree,  the  bird  when  shot 
to  fall  to  the  ground,  and  hail  to  descend  from  the  clouds, 
certainly  it  is  possible,  thought  Newton,  that  it  may  hold 
the  moon  in  her  orbit,  by  continually  bending  her  path  round 
the  earth.  If  so,  the  moon  must  perpetually  be  falling 
from  the  straight  line  in  which  she  would  travel,  were  the 
central  force  not  acting.  Force"  can  be  measured  by  the 
change  of  place  it  produces.  At  the  surface  of  the  earth, 
about  4000  miles  from  the  center  of  attraction,  bodies  fall 
1 6.  i  feet  in  the  first  second  of  time.  But  our  satellite  is 
240,000  miles  away,  or  60  times  more  distant.  So  the 
moon,  if  held  by  the  same  attraction,  only  diminishing 
exa'etly  as  the  square  of  the  distance  increases,  should  fall 
away  from  a  straight  line 


(60  x  60) 


of  1 6. i  feet; 


that  is,  ^Q  of  an  inch.  Newton  calculated  how  much 
the  moon  actually  does  curve  away  from  a  tangent  to 
her  orbit  in  one  second,  and  he  found  it  to  be  precisely 
that  amount  (page  237).  So  the  law  of  gravitation  was 
immediately  established  for  the  moon ;  and  Newton's 
subsequent  work  showed  that  it  explained  equally  well 
the  motion  of  the  satellites  of  Jupiter  round  their  primary, 
and  the  motion  of  earth  and  all  other  planets  round  the 
sun.  He  found,  in  fact,  that  the  force  acting  depends,  in 
each  case,  on  the  product  of  the  masses  of  the  two  bodies, 
and  on  the  square  of  the  distance  between  them. 

Law  of  Gravitation  extends  also  to  the  Planets.  —  Newton 


Curvilinear  Motion  377 

by  no  means  considered  his  law  of  gravitation  established, 
just  because  it  explained  the  motion  of  the  moon  round 
the  earth.  If  the  law  is  universal,  it  must  completely 
account  for  the  movements  of  all  known  bodies  of  the 
solar  system  as  well.  Since  the  planets  travel  round  the 
sun  as  the  moon  does  round  the  earth,  a  force  directed 
toward  the  sun  must  continually  be  acting  upon  them. 
Is  not  this  the  force  of  gravitation  ?  Recall  Kepler's 
third  law.  Newton's  calculations  from  it  proved  that  the 
planets  fall  toward  the  sun  in  one  second  of  time  through 
a  space  which  is  less  for  each  planet  in  exact  proportion  as 
the  square  of  its  distance  from  the  sun  is  greater.  Also 
Kepler's  second  law  :  if  the  attracting  force  emanates  from 
the  sun,  the  planet's  radius  vector  will  pass  over  equal 
areas  in  equal  times.  On  the  other  hand,  it  cannot  pass 
over  equal  areas  in  equal  times,  if  the  center  of  attraction 
resides  in  any  direction  but  that  of  the  sun.  So  Kepler's 
second  law  shows  that  the  force  which 
attracts  the  planets  is  directed  toward 
the  sun.  What  chance  for  farther  doubt 
that  this  force  is  the  attraction  of  grav- 
itation of  the  sun  himself  ?  The  farther 
Newton's  investigations  were  pushed,  Apparatus  to  illustrate 

.,  A    ..   .  ~  , .  c  ,  .  Curvilinear  Motion 

the  more  striking  the  confirmation  of  his 
theory.  Historically,  the  three  laws  of  Kepler  expressed 
the  bare  facts  of  planetary  motion,  and  formed  the  basis 
upon  which  Newton  built  his  law -of  universal  gravitation. 
But  once  this  general  law  was  established,  it  was  seen 
that  Kepler's  laws  were  immediate  consequences  of  the 
Newtonian  law, — merely  special  cases  of  the  general 
proposition. 

Curvilinear  Motion  due  to  a  Central  Attracting  Force. —  A  facile 
form  of  apparatus  will  help  to  make  clear  the  motion  of  a  body  in 
arcs  of  conic  sections  under  influence  of  a  central  attracting  force,  and 


378  Argument  for  Gravitation 

to  impress  it  upon  the  mind.  A  glass  plate  about  18  inches  in  diameter 
is  leveled  (preceding  page) ;  and  through  a  central  hole  projects 
the  conical  pole-piece  of  a  large  electro-magnet.  Smoke  the  upper 
face  of  the  glass  plate  evenly  with  lampblack.  Connect  battery  circuit, 
and  the  apparatus  is  ready  for  experiment.  Project  repeatedly  across 

the  plate  at  different  velocities  a  small 
bicycle  ball  of  polished  steel,  aimed  a 
little  to  one  side  of  the  pole-piece.  It 
is  convenient  to  blow  the  ball  out  of  a 
stout  piece  of  glass  tubing,  held  in  the 
plane  of  the  plate.  The  ball  then 
leaves  its  trace  upon  the  plate,  as  this 
figure  shows ;  and  the  form  of  orbit  is 
purely  a  question  of  initial  velocity. 
Lowest  speed  gives  a  close  approach 
to  the  ellipse  with  the  pole-piece  at 
one  of  its  foci :  friction  of  the  ball  in 

Experimental  O^Tactually  obtained    the  lampblack  will  reduce  the   velocity 

with  this  Apparatus  so  that  the  ball  is  likely  to  be  drawn 

in  upon   the   center  of  attraction,  on 

completing  one  revolution.  A  higher  speed  gives  the  parabola,  whose 
form  is  also  somewhat  modified  by  unavoidable  lessening  of  the  ball's 
velocity ;  and  still  higher  initial  velocities  produce  the  two  hyperbolas, 
C  and  D.  This  ingenious  experiment  is  due  to  Wood.  The  true  form 
of  all  these  curves  is  given  on  page  397. 

Mutual  Attractions. — One  farther  step  had  to  be  taken, 
to  apply  Newton's  third  law  of  motion  to  the  case  of  sun, 
moon,  and  planets.  This  law  states  that  whenever  one 
body  exerts  a  force  upon  another,  the  latter  exerts  an 
equal  force  in  the  opposite  direction  upon  the  first.  Earth, 
then,  cannot  attract  moon  without  moon's  also  attracting 
earth  with  an  equal  force  oppositely  directed.  Sun  can- 
not attract  earth  unless  earth  also  attracts  sun  in  a  similar 
manner.  So,  too,  the  planets  must  attract  each  other; 
and  if  they  do,  their  motions  round  the  sun  must  be 
mutually  disturbed,  in  accordance  with  the  second  law  of 
motion.  Kepler's  laws,  then,  must  need  some  slight 
change  to  fit  them  to  the  actual  case  of  mutual  attractions. 
But  it  was  known  from  observation  that  the  planets  deviate 


Center  of  Gravity  of  Earth-Moon         379 

slightly  from  Kepler's  laws  in  going  round  the  sun.  The 
question,  then,  arose  whether  deviations  really  observed 
are  precisely  matched  by  calculated  attractions  of  planets 
upon  each  other.  Newton  could  not  answer  this  question 
completely,  because  the  mathematics  of  his  day  was  in- 
sufficiently developed ;  but  over  and  over  again,  Termed 
observations  of  moon  and  planets  since  his  time  have  been 
compared  with  theories  of  their  movements  founded  on 
Newton's  law  of  universal  gravitation,  as  interpreted  by 
the  higher  mathematics  of  a  later  day,  until  the  establish- 
ment of  that  law  has  become  complete  and  final.  Essen- 
tially everything  is  accounted  for.  And  unexpected  and 
triumphant  verification  came  with  the  discovery  of  Nep- 
tune in  1846;  for  this  proved  that  the  law  of  mutual 
attractions  was  capable,  not  only  of  explaining  the  motions 
of  known  bodies,  but  of  pointing  out  an  unknown  planet 
by  disturbance  it  produced  in  the  motion  of  a  known  and 
neighboring  one. 

Earth  and  Moon  revolve  round  their  Common  Center  of 
Gravity.  —  It  has  been  said  that  the  moon  revolves  round 
the  earth.  This  statement  needs  modification,  and  it 
admits  of  ready  illustration.  Strictly  speaking,  the  moon 
revolves,  not  round  the  earth,  but  round  the  center  of 
gravity  of  earth  and  moon  considered  as  a  system  or  unit. 
And  as  moon's  attraction  for  earth  is  equal  to  earth's 
for  moon,  the  center  of  our  globe  must  revolve  round  that 
center  of  gravity  also. 

Cut  a  cardboard  figure  like  that  in  next  illustration  —  exact  size  ines- 
sential. Its  center  of  gravity  will  lie  somewhere  on  the  line  joining  the 
centers  of  the  two  disks,  and  is  easily  found  by  trial,  puncturing  the  card 
with  a  pin  until  point  is  found  where  disks  balance  each  other,  and 
gravity  has  no  tendency  to  make  the  card  swing  round.  This  point 
will  be  the  center  of  gravity.  Around  it  describe  a  circle  passing 
through  center  of  large  disk ;  and  from  the  same  center  describe  also 
an  arc  passing  through  center  of  smaller  disk.  Twirl  the  card  round 


38o 


Argument  for  Gravitation 


its  center  of  gravity,  by  means  of  a  pencil  or  penholder  ;  or  the  card 
may  be  projected  into  the  air,  spinning  horizontally,  and  allowed  to  fall 

to  the  floor  :  these  circular 
arcs,  then,  represent  paths  in 
space  actually  traversed  by 
centers  of  earth  and  moon. 
To  find  where  center  of  grav- 
ity of  earth-moon  system  lies 
in  the  real  earth,  recall  that 
the  mass  of  our  globe  is  81 
times  that  of  the  moon. 
Moon's  center  is  therefore  81 
times  as  far  from  center  of 
gravity  of  the  system  as 
earth's  center  is.  This  places 
the  common  center  at  a  con- 
tinually shifting  point  always 
within  the  earth,  and  at  an 
average  distance  of  1000  miles 
below  that  place  on  its  sur- 
face where  the  moon  is  in 
the  zenith.  That  the  earth 

really  does   swing   round   in 
Motion  of  Center  of  Gravity  of  Earth-Moon  ^      m(mthly     ^      ^^ 

6000  miles  in  diameter  is  a  fact   readily  and  abundantly  verified  by 
observation. 


The  Newtonian  Law  of  Universal  Gravitation.  —  If  this 
attraction  for  common  things,  possessed  by  the  earth  and 
called  gravity,  extends  to  the  moon";  if  the  same  force, 
only  greater  on  account  of  greater  mass  of  central  body, 
controls  the  satellites  of  Jupiter  in  their  orbits  ;  if  the 
same  attraction,  greater  still  on  account  of  the  yet  greater 
mass  of  the  sun,  holds  all  the  planets  in  their  paths 
around  him,  may  it  not  extend  even  to  the  stars  ?  But 
these  bodies  are  so  remote  that  excessive  diminution  of 
the  sun's  gravitation,  in  accordance  with  the  law  of  inverse 
squares,  would  render  that  force  so  weak  as  to  be  unable 
to  effect  any  visible  change  in  their  motion,  even  in  thou- 
sands of  years.  As  observed  with  the  telescope,  motions 


Gravitation  alone  Sufficient  381 

of  certain  massive  stars  relatively  near  each  other  do, 
however,  uphold  the  Newtonian  law.  No  reason,  there- 
fore, exists  for  doubting  its  sway  throughout  the  whole  uni- 
verse of  stars.  If  we  pass  from  the  infinitely  great  to 
the  infinitely  little,  dividing  and  subdividing  matter  as  far 
as  possible,  each  particle  still  has  weight,  and  therefore 
must  possess  power  of  attraction.  Gravity,  then,  attracts 
each  particle  to  the  earth,  and  in  accordance  with  the 
third  law  of  motion,  each  particle  must  attract  the  earth 
in  turn  and  equally.  So  the  gravitation  of  earth  and 
moon,  for  example,  is  really  the  mutual  attraction  of  all  the 
particles  composing  both  these  bodies.  In  its  universality, 
then,  this  simple  but  all-comprehensive  law  may  finally  be 
written :  Every  particle  of  matter  in  the  universe  attracts 
every  other  particle  with  a  force  exactly  proportioned  to 
the  product  of  the  masses,  and  inversely  as  the  square  of 
the  distance  betiveen  them. 

Curvilinear  Motion :  No  Propelling  Force  needed.  — 
Newton's  theory  amounts  simply  to  this :  Granted  that 
planets  and  satellites  were  in  the  beginning  set  in  motion 
(it  does  not  now  concern  us  in  what  manner),  then  the 
attraction  of  gravitation  —  of  the  sun  for  all  the  planets 
and  of  each  planet  for  its  satellites  —  completely  accounts 
for  the  curved  forms  of  their  orbits,  and  for  all  their 
motions  therein.  It  may  be  supposed  that  the  state  of 
motion  was  originally  impressed  upon  these  bodies  by 
a  projectile  force,  or  that  their  present  motions  are  a 
resultant  inheritance  from  untold  ages  of  development 
of  the  solar  system  from  the  original  solar  nebula,  in 
accordance  with  the  working  of  natural  laws.  Once  set 
in  motion,  however,  Newton's  theory  suffices  to  show  that 
there  is  no  propelling  or  other  force  always  pushing  from 
behind,  nor  is  the  action  of  any  such  force  at  all  necessary 
to  keep  them  going.  Once  started  with  a  certain  velocity, 


382  Argument  for  Gravitation 

the  uninterrupted  working  of  gravitation  maintains  every 
body  continually  in  motion  round  its  central  orb.  In  one 
part  of  its  elliptic  path,  a  planet,  for  example,  may  recede 
from  the  sun,  but  the  sun  again  pulls  it  back ;  afterward  it 
again  recedes,  but  equally  again  it  returns,  perihelion  and 
aphelion  perpetually  succeeding  each  other.  Gravitation 
alone  explains  perfectly  and  completely  all  motions  known 
and  observed. 

Why  the  Earth  does  not  fall  into  the  Sun. —  Draw 
several  arrows  tangent  to  the  ellipse  at  different  points, 
to  show  in  each  case  the  direction  in 
which  earth  is  going  when  at  that 
point.  From  these  points  of  tangency 
draw  dotted  lines  toward  that  focus 
where  the  sun  is,  to  represent  direction 
in  which  gravitation  is  acting.  It  is 

Earth  is  never  moving  di- 
rectly toward  the  Sun  apparent  that  the  planet  is  never  mov- 
ing directly  toward  the  sun,  but  always 
at  a  very  large  angle  with  the  radius  vector ;  greatest  at 
perihelion,  B,  and  aphelion,  D,  where  it  becomes  a  right 
angle.  There  the  sun  is  powerless  either  to  accelerate  or 
retard.  According  to  Kepler's  second  law,  velocity  in  orbit 
is  continually  increasing  from  aphelion  to  perihelion,  be- 
cause gravitation  is  acting  at  an  acute  angle  with  the  direc- 
tion of  motion  A.  Therefore  earth's  motion  is  all  the  time 
accelerated,  until  it  reaches  perihelion.  Here  velocity  is  a 
maximum,  because  the  sun's  attraction  has  evidently  been 
helping  it  along,  ever  since  leaving  aphelion.  Gravitation 
of  the  sun,  too,  has  increased,  exactly  as  the  square  of  the 
planet's  distance  has  decreased.  Calculating  these  two 
forces  at  perihelion,  it  is  found  that  earth's  velocity  makes 
the  tendency  to  recede  even  stronger  than  the  increased 
attraction  of  the  sun ;  so  that  our  planet  is  bound  to  pass 
quickly  by  its  nearest  point  to  the  sun,  and  recede  again 


Strength  of  Solar  Attraction  383 

to  aphelion.  On  reaching  its  farthest  point,  relation  of 
the  two  forces  is  reversed ;  velocity  has  been  diminishing 
all  the  way  from  perihelion,  because  gravitation  is  acting 
at  an  obtuse  angle  with  direction  of  motion,  C.  The  earth 
is  all  the  time  retarded,  gravitation  holding  it  back,  until 
at  apheliqn  its  velocity  is  so  much  lessened  that  even  the 
enfeebled  attraction  of  the  sun  overpowers  it,  and  there- 
fore begins  to  draw  the  earth  toward  perihelion  again. 
So  all  the  planets  are  perpetually  preserved  (i)  against 
falling  into  the  sun,  and  (2)  against  receding  forever 
beyond  the  sphere  of  his  attraction.  At  points  where 
both  these  catastrophes  at  first  seem  most  likely  to  occur, 
direction  of  planet's  motion  is  always  exactly  at  right 
angles  to  the  attracting  force ;  thus  is  assured  that  curva- 
ture of  orbit  requisite  to  carry  it  farther  away  from  the 
sun  in  the  one  case,  and  in  the  other  to  bring  it  back 
nearer  to  him. 

Strength  of  the  Sun's  Attraction.  —  It  was  shown  on  page  144  that 
the  earth,  in  traveling  18^  miles,  is  bent  from  a  truly  straight  course 
only  one  ninth  of  an  inch  by  the  sun's  attraction.  So  it  might  seem 
that  the  force  is  not  very  intense  after  all.  But  by  calculating  it  and 
converting  it  into  an  equivalent  strain  on  ordinary  steel,  it  has  been 
found  that  a  rod  or  cylinder  of  this  material  3000  miles  in  diameter 
would  be  required  to  hold  sun  and  earth  together,  if  gravitation  were  to 
be  annihilated.  Or,  if  instead  of  a  solid  rod,  the  force  of  attraction 
were  to  be  replaced  by  heavy  telegraph  wires,  the  entire  hemisphere  of 
the  earth  turned  toward  the  sun  would  need  to  be  thickly  covered  with 
them,  —  about  10  to  every  square  inch  of  surface.  But  the  necessity 
for  this  vast  quantity  of  so  strong  a  material  as  steel  becomes  apparent 
on  recalling  that  the  weight  of  the  earth  is  six  sextillions  of  tons,  while 
the  weight  of  the  sun  is  more  than  330.000  times  greater ;  and  the  stress 
between  them  is  equal  to  the  attraction  of  sun  and  earth  for  each 
other.  Gravitation  in  the  solar  system  must  be  thought  of  as  pro- 
ducing stresses  of  this  character  between  all  bodies  composing  it,  and 
taken  in  pairs;  stress  between  each  pair  being  proportional  to  the 
product  of  their  masses,  and  varying  inversely  as  the  square  of  the  dis- 
tance separating  them  varies.  Sun  disturbs  the  moon's  elliptic  motion 
greatly,  and  even  Venus,  Mars,  and  Jupiter  perturb  it  perceptibly. 


384  Argument  for  Gravitation 

What  is  Gravitation  ?  —  Distinction  is  necessary  between 
the  terms  gravity  and  gravitation.  On  page  88  it  was  shown 
that  gravity  diminishes  from  pole  to  equator,  on  account 
of  (i)  centrifugal  force  of  earth's  rotation,  and  (2)  oblate- 
ness  of  earth,  or  its  polar  flattening,  by  which  all  points 
on  the  equator  are  further  from  the  center  than  the  poles 
are.  Earth's  attraction  lessened  in  this  manner  is  called 
gravity.  Gravitation,  on  the  other  hand,  is  the  term  used 
to  denote  cosmic  attraction  in  accordance  with  the  New- 
tonian law,  between  all  bodies  of  the  universe  taken  in 
pairs,  and  depending  solely  upon  the  product  of  the  masses 
of  each  pair  and  the  distance  which  separates  them.  Do 
not  make  the  mistake  of  saying  that  Newton  discovered 
gravity,  or  even  gravitation  ;  for  that  would  be  much  like 
saying  that  Benjamin  Franklin  discovered  lightning.  Men 
had  always  seen  and  known  that  everything  is  held  down 
by  a  force  of  some  sort,  and  had  recognized  from  the 
earliest  times  that  bodies  possess  the  property  called 
weight.  What  Newton  did  do,  however,  was  to  discover 
the  universality  of  gravitation,  and  the  law  of  its  action 
between  all  bodies:  upon  all  common  objects  at  the  surface 
of  the  earth  ;  upon  the  moon  revolving  round  us ;  and  upon 
the  planets  and  comets  revolving  round  the  sun.  This 
cardinal  discovery  is  the  greatest  in  the  history  of  astron- 
omy. Great  as  it  is,  however,  it  is  not  final ;  for  Newton 
did  not  discover,  nor  did  he  busy  himself  inquiring,  what 
gravitation  is.  Indeed,  that  is  not  yet  known.  We  only 
know  that  it  acts  instantaneously  over  distances  whether 
great  or  small,  and  in  accordance  with  the  Newtonian  law ; 
and  no  known  substance  interposed  between  two  bodies 
has  power  to  interrupt  their  gravitational  tendency  toward 
each  other.  How  it  can  act  at  a  distance,  without  contact 
or  connection,  is  a  mystery  not  yet  fathomed. 

Weighing  a  Planet  that  has  a  Satellite.  —  If  a  planet  has 


Weighing  the  Planets  385 

a  satellite,  it  is  easy  to  find  the  mass,  or  quantity  of  matter 
in  terms  of  sun's  mass.  First  observe  mean  distance  of 
satellite  from  its  primary,  and  then  find  the  time  of  revo- 
lution. Cube  the  distance  of  any  planet  from  the  sun,  and 
divide  by  square  of  periodic  time ;  the  quotient  will  be 
the  same  for  every  planet,  according  to  Kepler's  third  law. 
Also  cube  the  distance  of  any  satellite  of  Saturn  from  the 
center  of  the  planet,  and  divide  by  the  square  of  its  time 
of  revolution  :  the  quotient  will  be  the  same  for  every  sat- 
ellite, if  distances  and  periodic  times  have  been  correctly 
measured.  Do  the  same  for  satellites  of  other  planets,— 
Mars,  Jupiter,  Uranus,  and  Neptune.  The  quotients  will 
be  proportional  in  each  case  to  mass  of  central  body  in 
terms  of  the  sun ;  in  the  case  of  Saturn,  for  example,  the 
quotient  for  each  satellite  will  be  3^^  that  for  sun  and 
planets.  The  sun,  then,  is  3501  times  more  massive  than 
Saturn,  as  found  by  A.  Hall,  Jr.  Similarly  may  be  found 
the  mass  of  any  other  planet  attended-  by  a  satellite.  It 
is  not  necessary  to  know  the  mass  of  the  satellite,  because 
the  principle  involved  is  simply  that  of  a  falling  body ;  and 
we  know,  in  the  case  of  the  earth,  that  a  body  weighing 
100  pounds  or  1000  pounds  will  fall  no  swifter  than  one 
which  weighs  only  10  pounds.  By  the  same  method,  too, 
binary  stars  are  weighed  (page  454),  when  their  distances 
from  each  other  and  times  of  revolution  become  known. 

Weighing  a  Planet  that  has  No  Satellite.  —  This  is  a 
much  more  difficult  problem  ;  fortunately  only  two  large 
planets  without  satellites  are  known,  —  Mercury  and  Venus. 
Their  masses  can  be  ascertained  only  by  finding  what  dis- 
turbances they  produce  in  the  motions  of  other  bodies  near 
them.  The  mass  of  Venus,  for  example,  is  found  by  the 
deviation  she  causes  in  the  motion  of  the  earth.  The  mass 
of  Mercury  is  found  by  the  perturbing  effect  upon  Encke's 
comet,  which  often  approaches  very  near  him.  The  New- 
TODD'S  ASTRON.  —  25 


386 


Argument  for  Gravitation 


tonian  law  of  gravitation  forms  the  basis  of  the  intricate 
calculations  by  which  the  mass  is  found  in  such  a  case. 
But  the  result  is  reached  only  by  a  process  of  tedious  com- 
putation and  is  never  certain  to  be  accurate.  Much  more 
precise  and  direct  is  the  method  of  determining  a  planet's 
mass  by  its  satellite. 

The  vast  difference  between  the  two  methods  was  illustrated  at  the 
Naval  Observatory,  Washington,  1877,  shortly  after  the  satellites  of 
Mars  were  discovered.  The  mass  of  that  planet,  as  previously  esti- 
mated from  his  perturbation  of  the  earth,  was  far  from  right,  although 
it  had  cost  months  of  figuring,  based  upon  years  of  observation.  Nine 
days  after  the  satellites  were  first  seen,  a  mass  of  Mars  very  near  the 
truth  was  found  by  only  a  half  hour's  facile  computation. 

Weighing  the  Sun. — In  weighing  the  planets,  the  sun 
is  the  unit.  Our  next  inquiry  is,  what  is  the  sun's  own 
weight  ?  How  many  times  does  the  mass  of  the  sun  ex- 
ceed that  of  the  earth  ?  Evidently  the  law  of  gravitation 
.  will  afford  an  answer  to  this  question 
if  we  compare  the  attraction  of  sun 
with  that  of  earth  at  equal  distances. 
At  the  surface  of  the  earth  a  body 
falls  1 6.  i  feet  in  the  first  second  of 
time.  Imagine  the  sun's  mass  all  con- 
centrated into  a  globe  the  size  of  the 
earth :  how  far  would  a  body  on  its 
surface  fall  in  the  first  second  ?  First 
recall  how  far  the  earth  falls  toward 
the  sun  (or  deviates  from  a  straight 
line)  in  a  second :  it  was  found  to  be 
0.0099  feet  (page  144).  This  is  deflec- 
tion produced  by  the  sun  at  a  distance 
of  93,000,000  miles.  But  we  desire  to  know  how  far  the 
earth  would  fall  in  a  second,  were  its  distance  only  4000 
miles  from  the  sun's  center;  that  is,  if  it  were  23,250  times 


WATER  OF 
PPOSITETIDE 


To  explain  the  Direct  and 
the  Opposite  Tides 


Explanation  of  the  Tides  387 

nearer.  Obviously,  as  attraction  varies  inversely  as  the 
square  of  the  distance,  it  would  fall  0.0099  x  [23>25°]2> 
or  5i35 1,5/0  feet  But  we  saw  that  the  earth's  mass 
causes  a  body  to  fall  16.1  feet  in  the  first  second;  there- 
fore the  sun's  mass  is  nearly  332,000  times  greater  than 
that  of  the  earth. 

Gravitation  explains  the  Tides.  —  According  to  the 
law  of  gravitation,  the  attraction  of  moon  and  earth  is 
mutual ;  moon  attracts  earth  as  well  as  earth  attracts 
moon.  Earth,  then,  may  be  considered  also  as  traveling 
round  the  moon  (page  380).  Therefore,  earth  falls  toward 
moon,  just  as  moon  in  going  round  earth  is  continually 
dropping  from  the  straight  line  in  which  it  would  move, 
if  gravitation  were  not  acting.  Imagine  the  earth  made 
up  of  three  parts  (opposite  page),  independent  and  free 
to  move  upon  each  other  :  (a)  the  waters  on  the  side  toward 
the  moon ;  (b)  the  solid  earth  itself ;  (c)  the  waters  on  the 
side  away  from  the  moon.  In  going  round  moon  or  sun, 
these  three  separate  bodies  would  fall  toward  it,  through 
a  greater  or  less  space  according  to  their  individual  dis- 
tance from  sun  or  moon.  Waters  of  the  opposite  tide, 
therefore,  would  fall  moonward  or  sunward  through  the 
least  distance,  waters  of  the  direct  tide  through  the  great- 
est distance,  and  the  earth  itself  through  an  intermediate 
distance.  The  resultant  effect  would  be  a  separation  from 
earth  of  the  waters  on  both  near  and  further  sides  of  it. 
As,  however,  the  real  earth  and  the  waters  upon  it  are  not 
entirely  independent,  but  only  partially  free  to  move  rela- 
tively to  each  other,  the  separation  actually  produced  takes 
the  form  of  a  tidal  bulge  on  two  opposite  sides.  These 
are  known  as  the  direct  and  the  opposite  tides. 

Tides  raised  by  the  Sun.  —  Besides  our  satellite  the  only 
other  body  concerned  in  raising  tides  in  the  waters  of  the 
earth  is  the  sun.  Newton  demonstrated  that  the  force 


388 


Argument  for  Gravitation 


which  raises  tides  is  proportional  to  the  difference  of 
attractions  of  the  tide-  raising  body  on  two  opposite  sides 
of  the  earth.  Also  he  showed  that  this  force  becomes  less 
as  the  cube  of  the  distance  of  tide-producing  body  grows 
greater.  It  is,  therefore,  only  a  small  portion  of  the  whole 
attraction,  and  the  sun  tide  is  much  exceeded  by  that  of  the 
moon.  To  ascertain  how  much  :  first  as  to  masses  merely, 
supposing  their  distances  equal,  sun's  action  would  be 


HIGHEST  TIDE 


HIGHEST  TIDE 


HIGHEST  TIDE 


HIGHEST  TIDE 


FULI.QMOON 
Spring  Tide  at  Full  Moon 


Spring  Tide  at  New  Moon 


26^  million  times  that  of  moon,  because  his  mass  is 
8 1  x  332,000  times  greater.  But  sun's  distance  is  also 
390  times  greater  than  the  moon's  ;  so  that 

26^  millions 
(390) 3 

expresses  the  ratio  of  sun  tide  to  moon  tide,  or  about  the 
relation  of  2  to  5. 

Sun  Tides  and  Moon  Tides  combined.  —  As  each  body 
produces  both  a  direct  and  an  opposite  tide,  it  is  clear  that 
very  high  tides  must  be  raised  at  new  moon  and  at  full 
moon,  because  sun  and  moon  and  earth  are  then  in  line. 


Luni-Solar  Tides 


389 


These  are  spring  tides  (or  high-rising  tides),  occurring,  as 
the  figures  opposite  show,  twice  every  lunation.  Similarly 
is  explained  the  formation  of  lesser  tides,  called  neap 
tides,  which  occur  at  the  moon's  first  and  third  quarters. 
Instead  of  conspiring  together  to  raise  tides,  the  attraction 
of  the  sun  acts  athwart  the  moon's,  so  that  the  resultant 
neap  tides  are  raised  by  the  difference  of  their  attractions, 
instead  of  the  sum.  Both  relations  of  sun,  moon,  and 


Neap  Tide  at  First  Quarter 


Neap  Tide  at  Last  Quarter 


earth  producing  such  tides  are  shown.  Considering  only 
average  distances  of  sun  and  moon,  spring  tides  are  to 
neap  tides  about  as  7  to  3.  For  the  earth  generally, 
highest  and  lowest  spring  tides  must  occur  when  both  sun 
and  moon  are  nearest  the  earth  ;  that  is,  when  the  moon 
at  new  or  full  comes  also  to  perigee,  about  the  beginning 
of  the  calendar  year.  The  complete  theory  of  tides  can 
be  explained  only  by  application  of  the  higher  mathe- 
matics. But  the  law  of  gravitation,  taken  in  connection 
with  other  physical  laws,  fully  accounts  for  all  observed 
facts ;  so  that  the  tides  form  another  link  in  the  chain 
of  argument  for  universal  gravitation. 


39°  Argument  for  Gravitation 

The  Cause  of  Precession.  —  Precession  and  its  effect  upon 
the  apparent  positions  of  the  stars  have  already  been  de- 
scribed and  illustrated  in  Chapter  vi.  This  peculiar  behav- 
ior of  the  earth's  equator  is  due  to  the  gravitation  of  sun 
and  moon  upon  the  bulging  equatorial  belt  or  zone  of  the 
earth,  combined  with  the  centrifugal  force  at  the  earth's 
equator.  As  equator  stands  at  an  inclination  to  ecliptic, 
this  attraction  tends,  on  the  whole,  to  pull  its  protuberant 
ring  toward  the  plane  of  the  ecliptic  itself.  But  the  earth's 
turning  on  its  axis  prevents  this,  and  the  resultant  effect  is 
a  very  slow  motion  of  precession  at  right  angles  to  the 
direction  of  the  attracting  force,  similar  to  that  exemplified 
by  attaching  a  small  weight  to  the  exterior  ring  of  a 
gyroscope.  Three  causes  contribute  to  produce  preces- 
sion :  if  the  earth  were  a  perfect  sphere,  or  if  its  equator 
were  in  the  same  plane  with  its  path  round  the  sun  (and 
with  the  lunar  orbit),  or  if  the  earth  had  no  rotation  on 
its  axis,  there  would  be  no  precession.  The  action  of 
forces  producing  precession  is  precisely  similar  to  that 
which  raises  the  tidal  wave ;  and,  accordingly,  solar  pre- 
cession takes  place  about  two  fifths  as  rapidly  as  that  pro- 
duced by  the  moon.  The  slight  attraction  of  the  planets 
gives  rise  to  a  precession  -^^  that  of  sun  and  moon. 

Nutation  of  the  Earth's  Axis.  —  Nutation  is  a  small  and  periodic 
swinging  or  vibration  of  the  earth's  poles  north  and  south,  thereby 
changing  declinations  of  stars  by  a  few  seconds  of  arc.  The  axis  of 
our  globe,  while  traveling  round  the  pole  of  the  ecliptic,  A,  has  a  slight 
oscillating  motion  across  the  circumference  of  the  circle  described  by 
precession.  So  that  the  true  motion  of  the  pole  does  not  take  place 
along  pp',  an  exact  small  circle  around  A  as  a.  pole,  but  along  a  wavy 
arc  as  shown  in  next  illustration.  The  earth's  pole  is  at  P  only  at  a 
given  time.  This  nodding  motion  of  the  axis,  and  consequent  undu- 
lation in  the  circular  curve  of  precession,  is  called  nutation.  The 
period  of  one  cross  oscillation  due  to  lunar  nutation  is  i8f  years,  so 
that  the  number  of  waves  around  the  entire  circle  is  greatly  in  excess 
of  the  proportion  represented  in  the  figure.  In  reality  there  are  nearly 


Nutation  Illustrated 


391 


1400  of  them.  Just  as  the  celestial  equator  glides  once  round  on  the 
ecliptic  in  25,900  years,  as  a  result  of  precession,  so  the  moon's  orbit 
also  slips  once  round  the  ecliptic  in  18^  years,  thereby  changing 
slightly  the  direction  of  moon's  attraction  upon  the  equatorial  pro- 
tuberance of  our  earth,  and  producing  nutation. 


Illustrating  Motion  of  the  Celestial  Pole  by  Nutation 

When  Newton  had  succeeded  in  proving  that  his  law  of 
universal  gravitation  accounted  not  only  for  the  motions  of 
the  satellites  round  the  planets,  for  their  own  motions 
round  the  sun,  for  the  rise  and  fall  of  the  tides,  and  for 
those  changes  in  apparent  positions  of  the  stars  occa- 
sioned by  precession  and  nutation,  evidence  in  favor  of 
his  theory  of  gravitation  became  overwhelming,  and  it  was 
thenceforward  accepted  as  the  true  explanation  of  all  celes- 
tial motions. 


CHAPTER    XV 

COMETS  AND    METEORS 

/'""XDMETS,  as  well  as  other  unusual  appearances  in  the 
heavens,  were  construed  by  very  ancient  peoples 
into  an  expression  of  disapproval  from  their  deities. 
'  Fireballs  flung  by  an  angry  God,'  they  were  for  centuries 
thought  to  be  '  signs  and  wonders,'  —  a  sort  of  celestial 
portent  of  every  kind  of  disaster.  The  downfall  of  Nero 
was  supposed  to  be  heralded  by  a  comet ;  and  for  centuries 
the  densest  superstition  clustered  about  these  objects. 

True  Theory  of  Comets  not  Modern.  —  Chaldean  star- 
gazers  were  apparently  the  sole  ancient  nation  to  regard 
comets  as  merely  harmless  wanderers  in  space.  The 
Pythagoreans  only,  of  the  old  philosophers,  had  some 
general  idea  that  they  might  be  bodies  obeying  fixed  laws, 
returning  perhaps  at  definite  intervals. 

Seneca  held  this  view,  and  Emperor  Vespasian  attempted  to  laugh 
down  the  popular  superstitions.  But  in  those  days,  far-seeing  utter- 
ances had  little  effect  upon  a  world  full  of  obstinate  ignorance.  Some 
of  the  old  preachers  proclaimed  that  comets  are  composed  of  the  sins 
of  mortals,  which,  ascending  to  the  sky,  and  so  coming  to  the  notice  of 
God,  are  set  on  fire  by  His  wrath.  Texts  of  Scripture  were  twisted 
into  apparent  proofs  of  the  supernatural  character  of  comets,  and  for 
seventeen  centuries  beliefs  were  held  that  fostered  the  worst  forms  of 
fanaticism.  Copernicus,  of  course,  refused  to  regard  comets  as  super- 
natural warnings,  but  the  i6th  century  generally  accepted  their  evil 
omen  as  a  matter  of  course.  By  the  middle  of  the  iyth  century  came 
the  dawn  of  changing  views,  although  even  as  late  as  the  end  of  that 
century,  knowledge  of  the  few  facts  known  about  comets  was  kept  so 
far  as  possible  from  students  in  the  universities,  that  their  religious 
beliefs  might  not  be  contaminated. 

392 


Discoveries  of  Comets 


393 


But  credence  began  to  be  given  to  the  statements  of 
Tycho  Brahe  and  Kepler  that  comets  were  supralunar,  or 
beyond  the  moon,  and  perhaps  not  so  intimately  concerned 
in  '  war,  pestilence,  and  fam- 
ine '  as  had  been  believed. 
Newton  farther  demonstrated 
that  comets  are  as  obedient  to 
law  as  planets;  and  with  his 
authoritative  statements  came 
the  full  daylight  of  the  modern 
view. 

Discoveries  of  Comets.  — 
Comets  are  nearly  all  dis- 
covered by  apparent  motion 
among  the  stars.  The  illustra- 


A  Comet  is  discovered  by  its  Motion 


tion  shows  the  field  of  view  of  a  telescope,  in  which  ap- 
peared each  night  two  faint  objects.  Upper  one  remained 
stationary  among  the  stars,  but  lower  one  was  recognized 

as  a  comet  because  it  moved, 
as  the  arrow  shows,  and  was 
seen  each  night  farther  to 
the  right.  A  century  ago, 
Caroline  Herschel  in  Eng- 
land, and  Messier  in  France, 
were  the  chief  discoverers  of 
comets.  Pons  discovered  30 
comets  in  the  first  quarter  of 
the  i  Qth  century. 

Among  other  noteworthy  Euro- 
pean l  comet-hunters  '  during    the 
middle  and  latter  half  of  this  cen- 
Eariy  View  of  Donati's  Comet  (1858)        tury  were    Brorsen,    Donati,   and 

Tempel.        In     America,      Swift, 

Brooks,  and  Barnard  have  been  preeminently  successful.  Between 
them  and  several  other  astronomers,  both  at  home  and  abroad,  the 


394 


Comets  and  Meteors 


entire   available   night-time  sky  is  parceled  out  for  careful  telescopic 
search,  and  it  is  not  likely  that  many  comets,  at  all  within  the  range 

of  visibility  from  the  earth,  escape  their 
critical  gaze.  Sweeping  for  comets  is 
an  attractive  occupation,  but  one  re- 
quiring close  application  and  much 
patience.  Large  and  costly  instruments 
are  by  no  means  necessary.  Messier 
discovered  all  his  comets  with  a  spy- 
glass of  2\  inches  diameter,  magnify- 
ing only  five  times ;  and  the  name  of 
Pons,  the  most  successful  of  all  comet- 
hunters,  a  doorkeeper  at  the  observa- 
tory of  Marseilles,  is  now  more  famous 
in  astronomy  than  that  of  Thulis,  the 
then  director  of  that  observatory,  who 
taught  and  encouraged  him. 


Telescopic  Comet  without  and  with 
Nucleus 


Halley's  Comet  (1835) 


Their  Appearance.  —  Usually  a 
comet  has  three  parts.  The 
nucleus  is  the  bright,  star-like 

point   which    is   the    kernel,    the    true,    potential   comet. 

Around  this  is  spread  the  coma,  a  sort  of  luminous  fog, 

shading  from  the  nucleus,  and 

forming  with  it  the  head.    Still 

beyond    is    the    delicate    tail, 

stretching    away    into    space. 

And  this  to  the  world  in  gen- 
eral is  the  comet  itself,  though 

always  the  least  dense  of  the 

whole.       Sometimes     entirely 

wanting,  or  hardly  detectible, 

the  tail  is  again  an  exten- 
sion millions  of  miles  long. 

Although     usually    a    single 

brush   of   light,   comets    have 

been  seen  with  no  less  than 

SIX   tails.  Head  of  Donati's  Comet  (18E8) 


Development  of  the   Tail 


395 


Changes  in  Appearance.  —  With  increase  in  a  comet's 
speed  on  approaching  the  sun  and  its  state  of  excitation, 
perhaps  electrical,  its  physical  appearance  changes  and 
develops  accordingly.  When 
remote  from  the  sun,  comets  are 
never  visible  except  by  aid  of  a 
telescope,  and  their  appearance 
is  well  shown  at  top  of  oppo- 
site page ;  but  on  approaching 
nearer  the  sun,  a  nucleus  will 
often  develop  and  throw  off  jets 
of  luminosity  toward  the  sun, 
sometimes  curving  round  and 
opening  like  a  fan.  On  rare 
occasions  the  comet  will  become 
so  brilliant  as  to  be  visible  in 
broad  daylight.  After  growth 
of  the  coma  comes  development 
of  the  tail ;  and  this  showy 
appendage  sometimes  reaches 
stupendous  lengths,  even  so 
great  as  sixty  millions  of  miles, 
growing  often  several  million 
miles  in  a  day. 

Development  and  Direction  of 
Tail.  —  It  is  not  a  correct  anal- 
ogy that  the  tail  streams  out 

behind    like    a    Shower  Of    Sparks       Tail  always  points  away  from  the  Sun 

from    a   rocket.      There    is   no 

medium  to  spread  the  tail ;  for  there  is  no  material  sub- 
stance like  air  in  interplanetary  space,  and  therefore  noth- 
ing to  sweep  the  tail  into  the  line  of  motion.  Explanation 
of  the  backward  sweep  of  the  tail,  nearly  always  away 
from  the  sun,  as  in  above  diagram,  is  found  in  the  fact  that 


396 


Comets  and  Meteors 


while  the  comet  is  attracted,  the  tail  is  probably  repell  d 
by  the  sun.  Rapid  growth  of  tail  upon  approaching  the 
sun  is  explainable  in  this  way :  the  comet  as  a  solid  is 
attracted ;  but  when  it  comes  near  enough  to  be  partly 
dissipated  into  vapor,  the  highly  rarefied  gas  is  so  repelled 
that  gravitation  is  entirely  overcome,  and  the  tail  streams 
visibly  away  from  the  sun,  as  long  as  it  is  near  enough  to 
have  part  of  its  substance  continually  turning  into  vapor. 
Receding,  the  great  heat  diminishes ;  and  the  tail  becomes 
smaller,  because  less  material  is  converted  into  vapor. 

Types  of   Cometary  Tails.  —  Bredichin  divides  tails  of 
comets  into  three  types:   (i)  those  absolutely  straight  in 

space,  or  nearly  so,  like  the 
tail  of  the  great  comet  of 
1843  ;  (2)  tails  gently  curved, 
like  the  broad  streamer  of 
Donati's  comet  of  1858  (page 
2°);  (3)  short  bushy  tails, 
curving  sharply  round  from 
the  comet's  'nucleus,  as  in 
Encke's  comet.  The  origin 
of  tails  of  the  first  type  is 
related  to  ejections  of  hy- 
drogen, the  lightest  element 
known,  and  the  sun's  repul- 
sive force  is  in  this  case  14 
times  stronger  than  his  gravi- 
tative  attraction.  The  slightly 
curved  tails  of  the  second  type  are  due  to  hydrocarbons 
repelled  with  a  force  somewhat  in  excess  of  solar  gravity. 
In  producing  the  sharply  curved  tails  of  the  third  type, 
the  sun's  repellent  energy  is  about  one  fifth  that  of  his 
gravity,  and  these  tails  are  formed  from  emanations  of  still 
heavier  substances,  principally  iron  and  chlorine. 


Types  of  Cometary  Tails  (Bredichin) 


Cometary   Orbits  397 

This  theory  permits  a  complete  explanation  of  a  comet's  possessing 
tails  of  two  different  types  ;  or  even  tails  of  all  three  distinct  types. 
An  excellent  photograph  of  comet  Rordame-Quenisset  (1893)  showed 
four  tails,  which  subsequently  condensed  into  a  single  one.  Evidently 
the  ejections  may  be  at  different  times  connected  with  hydrogen,  hydro- 
carbon, or  iron,  or  any  combination  of  these,  according  to  the  chemi- 
cal composition  of  substances  forming  the  nucleus. 

Observations  for  an  Orbit.  —  As  soon  as  a  new  comet  js 
discovered,  its  position  among  the  stars  is  accurately  ob- 
served at  once.     On  subsequent  evenings,  these  observa- 
tions   are    repeated ;    and    after ' 
three  complete  observations  have 
been  obtained,  the  precise  path 
of   the  comet  can   generally  be 
calculated.     This    path    will   be 
one  of  the  three  conic  sections : 

(1)  if  it  is  an  ellipse,  the  comet 
belongs  to  the  class  of  periodic 
comets,    and   the   length   of    its 
period    will   be    greater    as   the 

eccentricity  of  orbit  is  greater ;          Form  of  Cometary  orbits 

(2)  if  the  path  is  a  parabola,  the 

comet  will  retreat  from  the  sun  along  a  line  nearly  par- 
allel to  that  by  which  it  came  in  from  the  stellar  depths; 

(3)  if  a  hyperbola,  the  path3  of  approach  to  and  recession 
from  the  sun  will  be  widely  divergent. 

Cometary  Orbits.  —  Some  comets  are  permanent  members 
of  the  solar  system,  while  others  visit  us  but  once.  Three 
forms  of  path  are  possible  to  them,  —  the  ellipse,  the 
parabola,  and  the  hyperbola.  With  a  path  of  the  first  type 
only  can  the  comet  remain  permanently  attached  to  the 
sun's  family.  The  other  two  are  open  curves,  as  in  above 
diagram ;  and  after  once  swinging  closely  round  the  sun, 
and  saluting  the  ruler  of  our  solar  system,  the  comet  then 
plunges  again  into  unmeasured  distances  of  space. 


398 


Comets  and  Meteors 


Whether  or  not  an  orbit  is  a  closed  or  open  curve  depends  entirely 
upon  velocity.  If,  when  the  comet  is  at  distance  unity,  or  93,000,000 
miles  from  the  sun,  its  speed  exceeds  26  miles  a  second,  it  will  never 

come  back ;  if  less,  it  will 
return  periodically,  after  wan- 
derings more  or  less  remote. 
Very  often  the  velocity  of  a 
comet  is  so  near  this  critical 
value,  26  miles  a  second,  that 
it  is  difficult  to  say  certainly 
whether  it  will  ever  return  or 
not.  Many  comets,  however, 
do  make  periodical  visits 
which  are  accurately  foretold. 
The  form  and  position  of 
their  orbits  show  in  numer- 
ous instances  that  these 
comets  were  captured  by 
planetary  attraction,  which 
has  reduced  their  original 
velocity  below  26  miles  a  sec- 
ond, and  thus  caused  them 
to  remain  as  members  of  the 
solar  system  indefinitely,  and 
obedient  to  the  sun's  control. 

A  Projectile's  Path  is  a  Parabola  A     Projectile's     Path     is    a 

(From  an  Instantaneous  Photograph  by  Lovell)        Parabola.  —  This  proposition, 

demonstrated  mathematically 

from  the  laws  of  motion,  is  excellently  verified  by  observation  of  the 
exact  form  of  curves  described  by  objects  thrown  high  into  the  air. 
Resistance  of  the  atmosphere  does  not  affect  the  figure  of  the  curve 
appreciably,  unless  the  velocity  is  very  swift.  A  l  foul  ball '  frequently 
exhibits  the  truth  of  this  proposition  beautifully,  in  its  flight  from  the 
bat,  high  into  the  air,  and  then  swiftly  down  to  the  '  catcher,'  whom 
the  photograph  shows  in  the  act  of  catching  the  ball,  though  some- 
what exaggerated  in  size.  The  horizontal  line  above  the  parabola  is 
called  the  directrix,  and  the  vertical  line  through  the  middle  of  the 
parabola  is  its  axis.  One  point  in  the  axis,  called  the  focus,  is  as  far 
below  the  vertex  as  the  directrix  is  above  it.  This  curve  has  a  number 
of  remarkable  properties,  one  of  which  is  that  every  point  in  the  curve 
is  just  as  far  from  the  focus  as  it  is  perpendicularly  distant  from  the 
directrix  (shown  by  equality  of  the  dotted  lines).  Another  property, 
very  important  and  much  utilized  in  optics,  is  this :  from  a  tangent  at 
any  point  of  the  parabola,  the  line  from  this  point  to  the  focus  makes 


The  Periodic  Comets  399 

the  same  angle  with  the  tangent  that  a  line  drawn  from  the  point  of 
tangency  parallel  to  the  axis  does.  According  to  this  property,  parallel 
rays  all  converge  to  the  focus  of  a  reflector  (page  196). 

Direction  of  their  Motion.  —  Unlike  members  of  the  solar 
system  in  good  and  regular  planetary  standing,  comets 
move  round  the  sun,  some  in  the  same  direction  as  the 
planets ;  others  revolve  just  opposite,  that  is,  from  east 
to  west.  The  planes  of  cometary  orbits,  too,  lie  in  all  di- 
rections —  their  paths  may  be  inclined  as  much  as  90°  to 
the  ecliptic.  A  comet  can  be  observed  from  the  earth, 
and  its  position  determined,  only  while  in  that  part  of  its 
orbit  nearer  the  sun.  Generally  this  is  only  a  brief  interval 
relatively  to  the  comet's  entire  period,  because  motion 
near  perihelion  is  very  swift.  It  is  doubtful  whether  any 
comet  has  ever  been  observed  farther  from  the  sun  than 
Jupiter. 

Dimensions  of  Comets.  —  Nucleus  and  head  or  coma  of 
a  comet  are  the  only  portions  to  which  dimension  can 
strictly  be  assigned.  There  are  doubtless  many  comets 
whose  comae  are  so  small  that  we  never  see  them  —  prob- 
ably all  less  than  15,000  miles  in  diameter  remain  undis- 
covered. The  heads  of  telescopic  comets  vary  from  about 
25,000  to  100,000  miles  in  diameter  ;  that  of  Donati's  comet 
of  1858  was  250,000  miles  in  diameter,  and  that  of  the 
great  comet  of  181 1,  the  greatest  on  record,  was  nearly  five 
times  as  large.  Tails  of  comets  are  inconceivably  exten- 
sive, short  ones  being  about  10,000,000  miles  long,  and  the 
longest  ones  (that  of  the  comet  of  1882,  for  example)  exceed- 
ing 100,000,000.  To  realize  this  prodigious  bulk,  one  must 
remember  that  if  such  a  comet's  head  were  at  the  sun,  the 
tail  would  stretch  far  outside  and  beyond  the  earth. 

The  Periodic  Comets.  —  Comets  moving  round  the  sun 
in  well-known  elliptic  paths  are  called  periodic  comets. 
About  30  such  are  now  known,  with  periods  less  than  100 


400  Comets  and  Meteors 

years  in  duration,  the  shortest  being  that  of  Encke's  comet 
(3|-  years),  and  the  longest  that  of  Halley's  (about  76  years). 
Nearly  all  of  these  bodies  are  invisible  to  the  naked  eye, 
and  only  about  half  of  them  have  as  yet  been  observed  at 
more  than  a  single  return.  Nearly  as  many  more  comets 
travel  in  long  oval  paths,  but  their  periods  are  hundreds  or 
even  thousands  of  years  long,  so  that  their  return  to  peri- 
helion has  not  yet  been  verified. 

Planetary  Families  of  Comets.  —  When  periodic  comets 
are  classified  according  to  distance  from  the  sun  at  their 
aphelion,  it  is  found  that  there  is  a  group  of  several  corre- 
sponding to  the  distance  of  each  large  outer  planet  from 
the  sun.  Of  these,  the  Jupiter  family  of  comets  is  the 
most  numerous,  and  the  orbits  of  many  of  them  are  ex- 
cellently shown  on  the  opposite  page.  Without  much 
doubt,  these  comets  originally  described  open  orbits,  either 
parabolas  or  hyperbolas ;  but  on  approaching  the  sun,  they 
passed  so  near  Jupiter  that  he  reduced  their  velocity  below 
the  parabolic  limit,  and  they  have  since  been  forced  to 
travel  in  elliptical  orbits,  having  indeed  been  captured  by 
the  overmastering  attraction  of  the  giant  planet.  While 
Jupiter's  family  of  comets  numbers  18,  Saturn  similarly 
has  2,  Uranus  3,  and  Neptune  6. 

Groups  of  Comets.  —  Vagaries  in  structure  of  comets 
prevent  their  identification  by  any  peculiarities  of  mere 
physical  appearance.  Identity  of  these  bodies  then,  or 
the  return  of  a  given  comet,  can  be  established  only  by 
similarity  of  orbit.  In  several  instances  comets  have  made 
their  appearance  at  irregular  intervals,  traveling  in  one 
and  the  same  orbit.  They  could  not  be  one  and  the  same 
comet ;  so  these  bodies  pursuing  the  same  track  in  the 
celestial  spaces  are  called  groups  of  comets. 

The  most  remarkable  of  these  groups  consists  of  the  comets  of  1668, 
1843,  1880,  1882,  and  1887,  all  of  which  travel  tandem  round  the  sun. 


Jupiter's  Family  of  Comets.     (From  Professor  Payne's  Popular  Astronomy^ 
TODD'S  ASTRON.  — 26       401 


402 


Comets  and  Meteors 


Probably  they  are  fragments  of  a  comet,  originally  of  prodigious  size, 
but  disrupted  by  the  sun  at  an  early  period  in  its  history ;  because  the 
perihelion  point  is  less  than  500,000  miles  from  the  sun's  surface.  At 
this  distance  an  incalculably  great  disturbing  tidal  force  would  be  ex- 
erted by  the  sun  upon  a  body  having  so  minute  a  mass  and  so  vast  a 
volume  ;  and  separate  or  fragmentary  comets  would  naturally  result. 

Number  of  Comets.  —  In  the  historical  and  scientific 
annals  of  the  past,  nearly  1000  comets  are  recorded.  Of 
these  about  100  were  reappearances;  so  that  the  total  num- 
ber of  distinct  comets  known  and  observed  is  between  800 
and  900. 

During  the  centuries  of  the  Christian  era  preceding  the  eighteenth,  the 
average  number  was  about  30  each  century ;  but  nearly  all  these  were 
bright  comets,  discovered  and  observed  without  telescopes.  As  tele- 
scopes came  to  be  used  more  and  more,  70  comets  belong  to  the  eigh- 
teenth century,  and  nearly  300  to  the 
nineteenth.  Of  this  last  number,  less 
than  one  tenth  could  have  been  discov- 
ered with  the  naked  eye ;  so  that  the 
number  of  bright  comets  appears  to 
vary  but  little  from  century  to  century. 
The  number  of  telescopic  comets  found 
each  year  is  on  the  increase,  because 
more  observers  are  engaged  in  the 
search  than  formerly,  and  their  work  is 
done  in  accordance  with  a  carefully 
organized  system.  About  seven  com- 
ets are  now  observed  each  year.  Fewer 
are  found  in  summer,  owing  to  the 
short  nights.  During  the  2000  years 
—  although  but  <  a  minute  in  the  prob- 
able duration  of  the  solar  system '- 
the  comets  coming  within  reach  of  the  sun  must  be  counted  by  thou- 
sands ;  for  it  is  probable  that  about  1000  comets  pass  within  visible 
range  from  the  earth  every  century.  It  is  not,  however,  likely  that 
more  than  half  of  these  can  ever  be  seen . 

Remarkable  Comets  before  1850.  —  Comets  of  immense  proportions 
have  visited  our  skies  since  the  earliest  times.  Others  having  singular 
characteristics  must  be  mentioned  also.  Halley's  comet  is  famous 
because  it  was  the  first  whose  periodicity  was  predicted.  This  was  in 
1704,  but  the  verification  did  not  take  place  till  1759,  again  in  1835, 


Cheseaux's  Multi-tailed  Comet 
(1744) 


The  Lost  Bielas  Comet  403 

and  it  will  reappear  in  1910.  The  comet  of  1744  (opposite)  had  a 
fan-shaped,  multiple  tail.  The  great  comet  of  181 1  was  one  of  the  finest 
of  the  igth  century,  and  its  period  is  about  3000  years  in  duration.  In 
1818  Pons  discovered  a  very  small  comet,  which  has  become  famous 
because  of  the  short  period  of  its  revolution  round  the  sun  —  only  3$ 
years.  This  fact  was  discovered  by  Encke,  a  great  German  astronomer, 
and  the  comet  is  now  known  as  Encke's  comet.  It  has  been  seen  at 
every  return  to  perihelion,  three  times  every  ten  years.  Up  to  1868, 
the  period  of  Encke's  comet  was  observed  to  be  shortening,  by  about 
2\  hours,  at  each  return ;  and  this  diminution  led  to  the  hypothesis 
of  a  resisting  medium  in  space  —  not  well  sustained  by  more  recent 
investigations.  Encke's  comet  is  inconspicuous,  has  exhibited  remark- 
able eccentricities  of  form  and  structure,  and  is  now  invisible  without 
a  telescope.  Returns  are  in  1895,  1898,  and  1901.  The  great  comet 
of  1843,  perhaps  the  most  remarkable  of  all  known  comets,  was  visible 
in  full  daylight,  and  at  perihelion  the  outer  regions  of  its  coma  must 
have  passed  within  50,000  miles  of  the  surface  of  the  sun  —  nearer  than 
any  known  body.  At  perihelion,  its  motion  was  unprecedented  in 
swiftness,  exceeding  1,000,000  miles  an  hour.  Its  period  is  between  500 
and  600  years. 

The  Lost  Biela's  Comet.  —  Montaigne  at  Limoges,  France,  discov- 
ered in  1772  a  comet  which  was  seen  again  by  Pons  in  1805,  and  then 
escaped  detection  until  1826,  when  it 
was   rediscovered  and   thought  to  be 
new  by  an  Austrian  officer  named  Biela, 
by  whose  name  the  comet   has  since 
been  known.     He  calculated  its  orbit, 
and   showed   that   the  period   was   6V 
years.      At  reappearance  in    1845-46, 
it  was   seen   to    have   split   into   two 
unequal  fragments,  as  in  the  illustra- 
tion,   and    their    distance    apart    had        Biela's  Double  Comet  (1845-46) 
greatly  increased  when   next    seen   in 

1852.  At  no  return  since  that  date  has  Biela's  comet  been  seen;  and 
the  showers  of  meteors  observed  near  the  end  of  November  in  1872, 
1885,  and  1892,  are  thought  to  be  due  to  our  earth  passing  near  the 
orbit  of  this  lost  body,  and  to  indicate  its  further,  if  not  complete  dis- 
integration. These  meteors  are,  therefore,  known  as  the  Bielids  ;  also 
Andromedes,  because  they  appear  to  come  from  the  constellation 
of  Andromeda.  During  the  shower  of  1885,  on  the  27th  of  Novem- 
ber, a  large  iron  meteorite  fell,  and  was  picked  up  in  Mazapil,  Mexico. 
Without  doubt  it  once  formed  part  of  Biela's  comet. 

Remarkable   Comets   between    1850   and    1875. — In   1858  appeared 
Donates  comet,  which  attained  its  greatest  brilliancy  in  October,  having 


404 


Comets  and  Meteors 


a  tail  40°  long,  sharply  curved,  and  8°  in  extreme  breadth.  Also  there 
were  two  additional  tails,  nearly  straight,  and  very  long  and  narrow, 
as  shown  in  the  following  illustration.  Its  orbit  is  elliptic,  with  a 
period  of  nearly  2000  years.  In  1861  appeared  another  great  comet. 
Its  tail  was  fan-shaped,  with  six  distinct  emanations,  all  perfectly 
straight.  The  outer  ones  attained  the  enormous  apparent  length  of 
nearly  120°,  and  were  very  divergent,  owing  to  immersion  of  the  earth 

in  the  material  of  the  tail  to  a 
depth  of  300.000  miles.  This  comet 
also  travels  round  the  sun  in  an 
elliptic  path,  with  a  period  exceed- 
ing 400  years.  The  next  fine  comet 
appeared  in  1874,  and  is  known  as 
Coggia's  comet.  Its  nucleus  was 
of  the  first  magnitude,  and  its  tail 
50°  in  length,  and  very  slightly 
curved.  Coggia's  comet  was  the 
first  of  striking  brilliancy  to  which 
the  spectroscope  was  applied,  and 
it  was  found  that  its  gaseous  sur- 
roundings were  in  large  part  com- 
posed of  hydrogen  compounded 
with  carbon.  Coggia's  comet,  when 
far  from  perihelion,  presented  an 
anomalous  appearance,  well  shown 
in  the  opposite  illustration  —  a 
bright  streak  immediately  following 

the  nucleus  and  running  through  the  middle  of  the  tail.  When  nearer 
the  sun,  this  streak  was  replaced  by  the  usual  dark  one.  No  sufficient 
explanation  of  either  has  yet  been  proposed.  The  orbit  of  Coggia's 
comet  is  an  ellipse  of  so  great  eccentricity  that  this  body  cannot 
reappear  for  thousands  of  years. 

Remarkable  Comets  between  1875  and  1890.  —  Only  two  require 
especial  mention,  the  first  of  which  was  discovered  in  1881,  and  was  a 
splendid  object  in  the  northern  heavens  in  June  of  that  year.  It  was 
similar  in  type  to  Donati's  comet  of  1858,  and  was  the  first  comet  ever 
successfully  photographed.  In  1882  there  were  two  bright  comets,  one 
pf  them  in  many  respects  extraordinary.  So  great  was  the  intrinsic 
brightness  that  it  was  observed  with  the  naked  eye,  close  alongside 
the  sun.  Indeed,  it  passed  between  the  earth  and  the  sun,  in  actual 
transit ;  and  just  before  entering  upon  the  disk,  the  intrinsic  brightness 
of  the  nucleus  was  seen  to  be  scarcely  inferior  to  that  of  the  sun  itself. 
It  was  a  comet  of  huge  proportions.  Its  tail  stretched  through  space 
over  a  distance  exceeding  that  of  the  sun  from  the  earth,  and  parts  of 


Donati's  Triple-tailed  Comet  of  1858 


When    Will  the  Next  Comet  Come         405 


its  head  passed  within  300,000  miles  of  the  solar  surface,  at  a  speed 
of  200  miles  a  second.  Probably  this  near  approach  explains  what  was 
seen  to  take  place  on  recession  from  the  sun  —  the  breaking  up  of  the 
comet's  head  into  several  separate  nuclear  masses,  each  pursuing  an 
independent  path.  Also  this  comet's  tail  presented  a  variety  of  unusual 
phenomena,  at  one  time  being  single  and  nearly  straight,  while  again 
there  were  two  tails  slightly  curved. 
Besides  this,  its  coma  was  sur- 
rounded by  an  enormous  sheath  or 
envelope  several  million  miles  long, 
extending  toward  the  sun. 

Remarkable  Comets  since  1890.— 
No  very  bright  comet  appeared 
between  1882  and  1897;  but  the 
Brooks  comet  of  1893,  although  a 
faint  one  and  at  no  time  visible  to 
the  naked  eye,  is  worthy  of  note 
because  of  some  remarkable  photo- 
graphs of  it  obtained  by  Barnard. 
The  illustration  (next  page)  is  re- 
produced from  one  of  them,  and 
enlarged  from  the  original  negative. 
Changes  in  this  comet  were  rapid 
and  violent,  and  the  tail  appeared 
broken  and  distorted,  like  '  a  torch 
flickering  and  streaming  irregularly 
iii  the  wind.1  Ejections  of  matter  from  the  comet's  nucleus  may  have 
been  irregular  or  it  may  have  encountered  some  obstacle  which  shat- 
tered it  —  perhaps  a  swarm  of  meteors. 

When  will  the  Next  Comet  come  ?  —  If  a  large  bright 
comet  is  meant,  the  answer  must  be  that  astronomers 
cannot  tell.  One  may  blaze  into  view  at  almost  any  time. 
During  the  latter  half  of  the  iQth  century,  bright  comets 
have  come  to  perihelion  at  an  average  interval  of  about 
seven  years.  But  already  ( 1 897)  this  interval  has  been  more 
than  doubled  since  the  last  great  comet  (1882).  A  bright 
one  is  certain,  however,  in  1910,  because  Halley's  periodic 
comet,  last  seen  in  1835,  will  return  in  that  year.  Of  the 
lesser  and  fainter  periodic  comets,  several  return  nearly 
every  year ;  but  they  are  for  the  most  part  telescopic,  and 


Drawings  of  Coggia's  Comet  (1874) 


406 


Comets  and  Meteors 


rarely  attract  the  attention  of  any  one  save  the  astronomers. 
Three  are  due  in  1898,  and  five  in  1899. 

Light  of  Comets.  —  The  light  of  comets  is  dull  and  feeble, 
and  not  always  uniform.  When  in  the  farther  part  of 
their  orbits,  comets  seem  to  shine  only 
by  light  reflected  from  the  sun ;  and 
that  is  why  they  so  soon  become  invis- 
ible, on  going  away  from  perihelion. 
They  are  then  bodies  essentially  dark 
and  opaque.  But  with  approach  to- 
ward the  sun,  the  vast  increase  in  bright- 
ness, often  irregular,  is  due  to  light 
emitted  by  the  comet  itself,  and  it  is 
this  intrinsic  brightness  of  comets, 
that,  for  the  most  part,  makes  them 
the  striking  objects  they  are.  In  some 
manner  not  completely  understood,  radia- 
tions of  the  sun  act  upon  loosely  com- 
pacted materials  of  the  comet's  head, 
producing  a  luminous  condition  which, 
in  connection  with  the  repulsive  force 
exerted  by  that  central  orb  gives  rise  to 
all  the  curious  phenomena  of  the  heads 
and  tails  of  comets. 

Chemical  Composition.  —  Through 
analysis  of  the  light  of  comets  by  the 
spectroscope,  it  is  known  that  the  chief 
element  in  their  composition  is  carbon, 
combined  with  hydrogen ;  that  is,  hydro- 
carbons. The  elements  so  far  found  are 
few.  Sodium,  magnesium,  and  iron  were 
found  in  the  great  comet  of  1882;  also  nitrogen,  and 
probably  oxygen.  It  is  not  certain  that  the  spectrum  of 
a  comet  remains  always  the  same;  perhaps  there  are 


Brooks 's  Comet  of 

1893   (photographed 

by  Barnard) 


Cornels  Discovered  during  Eclipses         407 

rapid  changes  on  approaching  the  sun.  The  faint  contin- 
uous spectrum,  a  background  for  brighter  lines  in  the  blue, 
green,  and  yellow,  is  reflected  sunlight. 

The  illustration  shows  a  part  of  the  spectrum  of  the  comet  of  1882, 
with  the  Fraunhofer  lines  G,h,H,K,  and  others,  whose  presence  dis- 
tinctly confirms  this  hypothesis.  The  spectra  of  between  20  and  30 
comets  have  been  observed  in  all,  and  they  appear  to  have  in  general 
very  nearly  the  same  chemical  composition. 


37 


Spectrum  of  Comet  of  1882  (Sir  William  Huggins) 

Photographing  Comets. — The  light  of  a  comet  is  usually  feeble,  at 
least  so  far  as  the  eye  is  concerned,  and  its  actinic  power  is  even  less. 
How  then  can  a  comet  be  photographed?  Evidently  in  one  of  two 
ways  only.  Either  the  photographic  plate  must  be  very  sensitive,  or 
the  exposure  must  be  very  long.  Before  invention  of  the  modern 
sensitive  dry  plate,  it  had  been  found  impossible  to  photograph  comets. 
The  first  photograph  of  a  comet  was  made  by  Henry  Draper,  who 
photographed  the  comet  of  1880.  Since  1890  many  faint  comets  have 
been  successfully  photographed  at  the  Lick  Observatory,  and  elsewhere, 
by  the  use  of  very  sensitive  plates  and  a  long  exposure.  Next  illus- 
tration shows  a  photograph  of  Gale's  comet  (1894),  in  which  the  expo- 
sure was  prolonged  to  I  h.  o  m.  The  comet  was  moving  rapidly,  and 
as  the  clockwork  moving  the  telescope  was  made  to  follow  the  comet 
accurately,  all  stars  adjacent  to  it  appear  upon  the  photograph,  not  as 
points  of  light,  but  as  parallel  trails  of  equal  length.  Henry  and  Wil- 
son have  met  with  equal  success. 

Comets  discovered  during  Eclipses.  —  Probably  more 
than  one  half  of  all  comets  coming  within  range  of 
visibility  from  earth  remain  undiscovered,  because  of  the 
overpowering  brilliancy  of  the  sun.  Ought  not,  then,  new 
comets  to  be  discovered  during  total  eclipses  of  the  sun  ? 
This  has  actually  happened  on  at  least  two  such  occasions, 
and  a  like  appearance  has  been  suspected  on  two  more. 


408 


Comets  and  Meteors 


During  the  total  eclipse  of  the  i;th  of  May,  1882,  observed  in  Egypt, 
Schuster  photographed  a  new  comet  alongside  the  solar  corona,  as 
shown  on  page  301.  This  comet  was  named  for  Tewfik,  who  was  then 
khedive.  Also  another  comet  was  similarly  photographed,  but  joining 
immediately  upon  the  streamers  of  the  corona,  during 
the  total  eclipse  of  the  i6th  of  April,  1893,  by  Schaeberle 
in  Chile.  Both  of  these  comets  were  new  discoveries, 
and  neither  of  them  has  since  been  seen.  As  there  is 
but  one  observation  of  each,  nothing  is  known  about 
their  orbits  round  the  sun,  nor  whether  they  will  ever 
return. 

Mass  and  Density.  —  So  small  are  the  masses 
of  comets  that  only  estimates  can  be  given  as 
compared  with  the  mass  of  the  earth.    Comets 
have  in  certain  instances  approached  very  near 
to  lesser  bodies  of  the  solar  system ;  but  while 
cometary  orbits  and  motions  have  been  greatly 
disturbed   thereby,  no   change    has   been    ob- 
served   in    the    motion    of    satellites   or   other 
bodies  near  which  a  comet  has   passed.     So 
this  mass  must  be  slight.     Probably  no  comet's 
mass  is  so  great  as  the  T^oWo   Part  of   the 
earth's ;  but  even  if  only  one  third  of  this,  it 
would   still  equal  a  ball  of  iron   100  miles  in 
diameter.     If  the  mass  of  comets  is  so  small, 
while  their  volume  is  so  vast,  what  must  be 
the  density  of  these  bodies  ?     For  the  density 
is  equal  to  the  mass  divided  by  the  volume, 
Gale's  comet     anc^   comets   must,   therefore,   be    exceedingly 
thin    and    tenuous.     On    those  rare  occasions 
when  stars  have  been  observed  through  the 
tail  of  a  comet,  although  it  may  be  millions 
of    miles   in    thickness,  still    no  diminution  of   the    star's 
luster  has  been  perceived.     Even  through  the  denser  coma 
the  light  of  a  star  passes  undimmed ;  though  the  star's 
image,  if  very  near  the  comet's  nucleus,  may  be  rendered 


of  1894 

(photographed 

by  Barnard) 


Collision  with  a  Comet  409 

somewhat  indistinct.  The  air  pump  is  often  used  to  pro- 
duce an  approach  to  a  perfect  vacuum  ;  but  in  a  cubic 
yard  of  such  vacuum  there  would  be  many  hundred  times 
the  amount  of  matter  in  a  cubic  yard  of  a  comet's  head. 

Passing  through  a  Comet's  Tail.  —  Curious  as  it  may 
seem,  these  enormous  tails  are  in  actual  mass  so  slight 
that  thrusting  the  hand  into  their  midst  would  bring  no 
recognition  to  the  sense  of  touch.  Collision  would  be 
much  like  an  encounter  with  a  shadow.  Comets'  tails 
are  excessively  airy  and  thin,  or,  as  Sir  John  Herschel 
remarks,  possibly  only  an  affair  of  pounds  or  even  ounces. 

The  mass  of  a  comet's  head  may  be  large  or  small ;  it  may  not  be 
more  than  a  very  large  stone,  or  in  the  case  of  the  larger  comets  it  is 
perfectly  possible  that  the  mass  of  the  head  should  be  composed  of  an 
aggregation  of  many  hundreds  or  even  thousands  of  small  compact 


I 


Earth  about  to  pass  through  Tail  of  Comet  of  1861 

bodies,  stony  and  metallic.  Usually  the  speed  is  so  great  that  the 
comet  itself  would  be  dissipated  into  vapor  on  experiencing  the  shock 
of  collision  with  any  of  the  planets.  In  at  least  two  instances  it  is 
known  that  the  earth  actually  passed  through  the  tail  of  a  comet,  once 
on  30th  June,  1861.  The  figure  shows  positions  of  sun  (6"),  head  of 
comet  (c),  and  earth  (/),  just  before  our  planet's  plunge  into  the  diaph- 
anous tail.  But  we  came  through  without  being  in  the  least  con- 
scious of  it,  except  from  calculations  of  the  comet's  position. 

Collision  with  a  Comet.  — As  the  orbits  of  comets  lie  at  all 
possible  inclinations  to  the  earth's  path,  or  ecliptic,  and  as 
the  motion  of  these  erratic  bodies  may  be  either  direct  or 
retrograde,  evidently  it  is  entirely  possible  that  our  planet 
may  some  time  collide  with  a  comet,  because  these  bodies 


4io  Comets  and  Meteors 

exist  in  space  in  vast  numbers.  As  but  one  collision  is 
likely  to  take  place  every  15,000,000  years,  the  chances 
are  immensely  against  the  happening  of  such  an  event  in 
our  time,  and  comets  are  not  dangerous  bodies.  '  If  one 
should  shut  his  eyes  and  fire  a  gun  at  random  in  the  air, 
the  chance  of  bringing  down  a  bird  would  be  better  than 
that  of  a  comet  of  any  kind  striking  the  earth/ 

However,  should  the  head  of  a  large  comet  collide  squarely  with  our 
globe  —  the  consequences  might  be  inconceivably  dire :  probably  the 
air  and  water  would  be  instantly  consumed  and  dissipated,  and  a  con- 
siderable region  of  the  earth's  surface  would  be  raised  to  incandescence. 
But  consequences  equally  malign  to  human  interests  might  result  from 
the  much  more  probable  encounter  of  the  earth's  atmosphere  with 
solid  particles  of  a  large  hydrocarbon  comet :  it  might  well  happen  that 
diffusion  of  noxious  gases  from  sudden  combustion  of  these  compounds 
would  so  vitiate  the  atmosphere  as  to  render  it  unsuitable  for  breathing. 
In  this  manner,  while  the  earth  itself,  its  oceans,  and  even  human  habi- 
tations, might  escape  unharmed,  it  is  not  difficult  to  see  how  even  a 
brush  from  the  head  of  a  large  comet  might  cause  universal  death  to 
nearly  all  forms  of  animal  existence. 

Origin  of  Comets.  —  The  origin  of  comets  is  still  shrouded  in  mys- 
tery. Probably  they  have  come  from  depths  of  the  sidereal  universe, 
and  so  are  entirely  extra-solar  in  origin.  Arriving  apparently  from 
all  points  of  space  in  their  journey  from  one  star  to  another,  they 
wheel  about  the  sun  somewhat  like  moths  round  a  candle.  Sometimes, 
as  already  shown,  they  speed  away  in  a  vast  ellipse,  with  the  promise 
of  a  future  visit,  though  at  some  date  which  cannot  be  accurately 
assigned.  Sometimes  they  continue  upon  interstellar  journeys  of  such 
vast  parabolic  dimensions,  perhaps  round  other  suns,  that  no  return 
can  ever  be  expected.  Probably  the  comets  are  but  chips  in  the  work- 
shop of  the  skies,  mere  waste  pieces  of  the  stuff  that  stars  are  made  of. 
It  has  been  urged,  too,  that  some  comets  may  have  originated  in  vapor- 
ous materials  ejected  by  our  own  sun,  or  the  larger  planets  of  our 
system ;  but  here  we  tread  only  the  vast  fields  of  mere  conjecture, 
tempting,  though  unsatisfying. 

Disintegration  of  Comets.  —  Every  return  to  perihelion 
appears  to  have  a  disintegrating  effect  upon  a  comet. 
In  a  few  cases  this  process  has  actually  been  taking 
place  while  under  observation;  for  example,  the  lost 


Meteors  and  Shooting  Stars     »          411 

Biela's  comet  in  1846,  the  great  comet  of  1882,  and 
Brooks's  comet  of  1889,  the  heads  of  which  were  seen 
either  to  divide  or  to  be  divided  into  fragments.  Groups 
of  comets  probably  represent  a  more  complete  disinte- 
gration. 

For  example,  the  comets  of  1843,  1880,  1882,  and  1887  travel  tandem, 
and  originally  were  probably  one  huge  comet.  In  the  case  of  still  other 
comets,  this  disintegration  has  gone  so  far  that  the  original  cometary 
mass  is  now  entirely  obliterated.  Instead  of  a  comet,  then,  there 
exists  only  a  cloud  of  very  small  fragments  of  cometary  matter,  too 
small,  in  fact,  to  be  separately  visible  in  space.  Such  interplanetary 
masses,  originally  single  comets  of  large  proportions,  have  by  their 
repeated  returns  to  the  sun  been  completely  shattered  by  the  oft- 
renewed  action  of  disrupting  forces  ;  and  all  that  is  now  left  of  them  is 
an  infinity  of  meteoric  particles,  trailing  everywhere  along  the  original 
orbit.  The  astronomer  becomes  aware  of  the  existence  of  these  small 
bodies  only  when  they  collide  with  our  atmosphere,  sometimes  pene- 
trating even  to  the  surface  of  the  earth  itself. 

Meteors,  Shooting  Stars,  and  Meteorites.  —  Particles  of 
matter  thought  to  have  their  origin  in  disintegrated  comets, 
and  moving  round  the  sun  in  orbits  of  their  own,  are 
called  meteors.  In  large  part,  our  knowledge  of  these 
bodies  is  confined  to  the  relatively  few  which  collide  with 
the  earth.  The  energy  of  their  motion  is  suddenly  con- 
verted into  heat  on  impact  with  the  atmosphere,  and  fric- 
tion in  passing  swiftly  through  it.  As  a  rule,  this  speedily 
vaporizes  their  entire  substance,  the  exterior  being  brushed 
off  by  the  air  as  soon  as  melted,  often  leaving  a  visible  train 
in  the  sky.  The  luminous  tracks  pass  through  the  upper 
atmosphere,  few  if  any  meteors  appearing  at  greater 
heights  than  100  miles,  and  few  below  30  miles.  These 
paths,  if  very  bright,  can  be  recorded  with  great  precision 
by  photography  as  Wolf,  Barnard,  and  Elkin  have  done. 
As  the  speed  of  meteors  through  the  air  is  comparable  with 
that  of  our  globe  round  the  sun,  we  know  that  their  motion 
is  controlled  by  the  sun's  attraction,  not  the  earth's. 


412  Comets  and  Meteors 

Very  small  meteors,  sometimes  falling  in  showers,  are  frequently 
called  shooting  stars,  but  the  late  Professor  Newton's  view  is  gradually 
gaining  ground,  that  there  is  no  definite  line  of  distinction.  The 
shooting  stars  are  thought  to  be  very  much  smaller  than  meteors, 
because  they  are  visible  for  only  a  second  or  two,  and  disappear 
completely  at  much  greater  heights  than  the  meteors  do.  Many 
millions  of  them  collide  with  our  atmosphere  every  day.  and  are 
quickly  dissipated.  Although  the  average  of  them  are  not  more  mas- 
sive than  ordinary  shot,  their  velocity  is  so  great  that  all  organic  beings, 
without  the  kindly  mantle  of  the  air  (were  it  possible  for  such  to  live 
without  it)  would  be  pelted  to  death.  If  a  meteor  passes  completely 
through  the  atmosphere,  and  reaches  the  surface  of  the  earth,  it  be- 
comes known  as  a  meteorite.  Many  thousand  pounds  of  such  inter- 
planetary material  have  been  collected  from  all  parts  of  the  earth, 
and  the  specimens  are  jealously  preserved  in  cabinets  and  museums, 
the  most  complete  of  which  are  in  London,  Paris,  and  Vienna.  Re- 
markable collections  in  the  United  States  are  at  Amherst  College, 
Harvard  and  Yale  Universities,  and  in  the  National  Museum  at 
Washington. 

Meteors  most  Abundant  in  the  Morning.  —  Run  rapidly  in  a  rain- 
storm :  the  chest  becomes  wetter  than  the  back,  because  of  advance 
of  the  body  to  meet  the  drops.  In  like  manner,  the  forward  or  advance 
hemisphere  of  the  earth,  in  its  motion  round  the  sun,  is  pelted  by  more 
meteors  than  any  other  portion.  As  every  part  of  the  earth  is  turned 
toward  the  radiant  during  the  day  of  24  hours,  it  is  obvious  that 
the  most  meteors  will  be  counted  at  that  hour  of  the  day  when  the 
dome  of  the  sky  is  nearly  central  around  the  general  direction  of  our 
motion  about  the  sun ;  in  other  words,  when  apex  of  earth's  way  is 

nearest  to  the  zenith.  Recall- 
ing  the  figures  on  pages  134- 
5,  it  is  apparent  that  this  takes 
place  about  sunrise ;  and  in 
the  adjacent  illustration, 
where  the  sun  is  above  the 
earth,  and  illuminating  the 
hemisphere  abd,  it  is  sunrise 

When  Meteors  are  most  Abundant^  at  d,  and  the  earth  _  is  speed- 

ing through  space  in  the  di- 
rection dp,  indicated  by  the  great  arrow.  So  the  hemisphere  adc  is 
advancing  to  meet  the  meteors  which  seem  to  fall  from  the  directions 
gSg.  If  we  suppose  meteoric  particles  evenly  distributed  throughout 
the  shoal,  the  number  becoming  visible  by  collision  with  our  atmos- 
phere will  increase  from  midnight  onward  to  six  in  the  morning,  pro- 
vided the  season  is  such  that  dawn  does  not  interfere.  From  noon  at 


The  Radiant  Point  4 1 3 

a  to  sunset  at  b,  there  would  be  a  gradual  decrease,  with  the  fewest 
meteors  falling  from  the  directions  fff,  upon  the  earth's  rearward 
hemisphere,  abc.  Also,  as  to  time  of  the  year,  it  is  well  known  that  our 
globe  encounters  about  three  times  as  many  shooting  stars  in  passing 
from  aphelion  to  perihelion  as  from  perihelion  to  aphelion. 

Radiant  Point. — On  almost  any  clear,  moonless  night, 
especially  in  April,  August,  November,  and  December,  a 
few  moments  of  close  watching  will  show  one  or  more 
shooting  stars.  Ordinarily,  they  appear  in  any  quarter  of 
the  sky ;  and  on  infrequent  occasions  they  streak  the 
heavens  by  hundreds  and  thousands,  for  hours  at  a  time, 
as  in  November  of  1799  and  1833.  These  are  known  as 
meteoric  showers.  Careful  watching  has  revealed  the  very 
important  fact,  that  practically  all  the  luminous  streaks  of 
a  shower,  if  prolonged  backward,  meet  in  a  small  area 
of  the  sky  which  is  fixed  among  the  stars.  Arrows  in  the 
following  figure  represent  the  visible  paths  of  20  meteors, 
and  the  direction  of  their  flight.  It  is  clear  that  lines  drawn 
through  them  will  nearly  all 
strike  within  the  ring.  This 
area  is  technically  known  as 
the  radiant  point,  or  simply 
the  radiant.  Divergence 
from  it  in  every  direction  is 
only  apparent — a  mere  effect 
of  perspective,  proving  that 
meteors  move  through  space 
in  parallel  lines.  The  radiant 
is  simply  the  vanishing  point. 
Notice  that  the  luminous  To  IIlustrate  the  Radiant  Point 

paths  are  longer,  the  farther  they  are  from  the  radiant ;  if 
a  meteor  were  to  meet  the  earth  head  on,  its  trail  would 
be  foreshortened  to  a  point,  and  charted  within  the  area  of 
the  radiant  itself.  About  300  such  radiant  points  are  now 


414 


Comets  and  Meteors 


known,  of  which  perhaps  50  are  very  well  established. 
The  constellation  in  which  the  radiant  falls  gives  the 
name  to  the  shower;  so  there  are  Leonids  and  Perseids, 
Andromedes  and  Geminids,  and  the  like. 

List  of  Principal  Meteor  Showers.  —  Following  is  given,  in  tabular 
form,  a  short  list  of  the  chief  meteoric  displays  of  the  year,  according  to 
Denning,  a  prominent  English  authority  :  — 

ANNUAL  SHOWERS  OF  METEORS 


POSITION  OF  RADIANT 

NAME  OF  SHOWER 

DATE  OF 
MAXIMUM 

DURATION  IN 
DAYS 

R  A. 

DECL. 

Quadrantids  .     . 

I5h.  19111. 

N.  53° 

Jan.      2 

2 

Lyrids  .... 

17      59 

N.  32 

April  1  8 

4 

Eta  Aquarids     . 

22        30 

S.       2 

May      2 

8 

Delta  Aquarids  .       22      38 

S.     12 

July    28 

3 

Perseids    .     .     . 

3        4 

N.  57 

Aug.    10 

35 

Orionids   .     .     . 

6       8 

N.  15 

Oct.     19 

10 

Leonids    .     .     . 

10           0 

N.  23 

Nov.   13 

2 

Andromedes 

I    41 

N.  43 

Nov.  26 

2 

Geminids  .     .     . 

7      12 

N.  33 

Dec.     7 

H 

When  more  than   one   radiant  falls   in  any  constellation,  the  usual 
designation  of  the  nearest  star  is  added,  to  distinguish  between  them. 

Paths  of  Meteors.  —  Repeated  observation  of  the  paths 
of  meteors  belonging  to  any  particular  radiant  soon  estab- 
lishes the  fact  that  showers  recur  at  about  the  same  time 
of  the  year.  Also  in  a  few  instances  the  shower  is  very 
prominently  marked  at  intervals  of  a  number  of  years. 
So  it  has  become  possible  to  predict  showers  of  meteors, 
which  on  several  occasions  have  been  signally  verified. 
Conspicuously  so  is  the  case  of  the  shower  of  November, 
1866,  which  came  true  to  time  and  place;  and  a  like 


Meteoric  Orbits 


415 


shower  is  confidently  predicted  for  I2th-I4th,  November, 
1899.     The  periodic  time  of  these  meteors  is  33^  years. 

The  position  of  their  radiant  among  the  stars,  and  the  direction  in 
which  the  meteors  are  seen  to  travel,  has  afforded  the  means  of  calcula- 
ting the  size  and  shape  of  their  orbit,  and  just  where  it  lies  in  space. 
The  figure  shows  the  orbit  of  the  Leonids,  or  November  meteors,  as 
related  to  the  paths  of  the  planets,  and  it  is  evident  that  these  bodies, 
although  they  pass  at  a  distance 
of  100,000,000  miles  from  the 
sun  at  their  perihelion,  recede 
about  i6|  years  later  to  a  dis- 
tance greater  than  that  of  Ura- 
nus. They  are  not  aggregated 
at  a  single  point  in  their  orbit, 
but  are  scattered  along  a  con- 
siderable part  of  it,  called  the 
'Gem  of  the  ring.1  As  the 
breadth  of  the  gem  takes  more 
than  two  years  to  pass  the  peri- 
helion point,  which  nearly  coin- 
cides with  the  position  of  the 
earth  in  the  middle  of  Novem- 
ber, there  will  usually  be  two  or 
three  meteoric  showers  at  yearly 
intervals,  while  the  entire  shoal 
is  passing  perihelion.  So  that 
lesser  showers  may  be  expected 
in  November  of  1898  and  1900, 
in  addition  to  the  chief  shower 
of  1899. 

Meteoric  Orbits  in  Space. 
—  But  it  must  not  be  in- 
ferred from  the  figure  here 
given  that  the  Leonids 
travel  in  the  plane  of  the 

planetary  orbits  ;  for,  at  the  time  when  their  distance 
from  the  sun  is  equal  to  that  of  the  planetary  bodies, 
they  are  really  very  remote  from  all  the  planets  except 
the  earth  and  Uranus.  This  is  because  of  the  large  angle 


Orbit  of  Comet  I  (1866)  and  of  the  Novem- 
ber Meteors 


416 


Comets  and  Meteors 


of   17°    by   which    the    orbit    of    the    November   meteors 
is  inclined  to  the  ecliptic.     It  stands  in  space  as  the  ad- 


Perihelion  Parts  of  Orbits  of  the  August  and  November  Meteor- showers 

jacent  figure  shows,  being  the  lower  one  of  the  two  orbits 
whose  planes  are  cut  off.  Similarly,  the  upper  and  nearly 
vertical  plane  represents  the  position  in  space  of  another 
meteoric  orbit,  which  intersects  our  path  about  loth 
August.  This  shower  is  therefore  known  as  the  August 
shower ;  also  these  meteors  are  often  called  Perseids. 


What  are  Meteors  417 

As  shown  by  the  arrows,  both  the  Perseids  and  the  Leonids  travel 
oppositely  to  the  planets ;  so  that  their  velocity  of  impact  with  our 
atmosphere  is  compounded  of  their  own  velocity  and  the  earth's  also. 
This  average  speed  for  the  Leonids,  about  45  miles  per  second,  is 
great  enough  to  vaporize  all  meteoric  masses  within  a  few  seconds  ; 
so  it  is  unlikely  that  a  meteoric  product  from  the  Leonids  will  ever  be 
discovered.  Impact  velocity  of  the  Andromedes  is  very  much  less, 
because  they  overtake  the  earth.  In  the  case  of  meteorites,  the  velocity 
of  ground  impact  probably  never  exceeds  a  few  hundred  feet  per  second, 
so  great  is  the  resistance  of  the  air;  and  several  meteoric  stones  which 
fell  in  Sweden,  1st  January,  1869,  on  ice  a  few  inches  thick,  rebounded 
without  either  breaking  it  or  being  themselves  broken. 

Connection  between  Comets  and  Meteors.  —  Not  long 
after  the  important  discovery  of  the  motion  of  meteors  in 
regular  orbits,  an  even  more  significant  relation  was  as- 
certained :  that  the  orbits  of  the  Perseids  and  the  Leonids 
are  practically  identical  with  the  paths  in  which  two  comets 
are  known  to  travel.  The  orbit  of  the  Leonids  is  coinci- 
dent with  that  of  Tempel's  comet  (1866  i),  and  the  Perseids 
pursue  the  same  track  in  space  with  Swift's  comet  (known 
as  1862  in).  The  latter  has  a  period  of  about  120  years, 
and  recedes  far  beyond  the  planet  Neptune.  So  do  the 
meteors  traveling  in  the  same  track.  They  are  much 
more  evenly  distributed  all  along  their  path  than  the 
Leonids  are ;  and  no  August  ever  fails  of  a  slight  sprinkle, 
although  the  shorter  nights  in  our  hemisphere  often  inter- 
fere with  the  display. 

What  are  Meteors  ?  —  Several  other  meteor  swarms  and 
comets  have  been  investigated  with  a  like  result ;  so  the 
conclusion  is  now  well  established  that  these  meteors,  and 
probably  all  bodies  of  that  nature,  are  merely  the  shattered 
residue  of  former  comets.  This  important  theory  is  con- 
firmed, whether  we  look  backward  in  the  life  of  a  comet, 
or  forward  :  if  backward,  comets  are  known  to  disintegrate, 
and  have  indeed  been  4  caught  in  the  act ' ;  if  forward,  our 
expectation  to  find  the  disruption  farther  advanced  in  the 
TODD'S  ASTRON.  —  27 


4i 8  Comets  and  Meteors 

case  of  some  comets  and  meteors  than  others  is  precisely 
confirmed  by  the  facts  regarding  different  showers.  Then, 
too,  as  will  be  shown  in  a  later  paragraph,  the  spectra 
of  meteorites  vaporized  and  photographed  in  our  lab- 
oratories are  practically  identical  with  the  spectra  of  the 
nuclei  of  comets.  The  conclusion  is,  therefore,  that  these 
latter  are  nothing  more  than  a  compact  swarm  or  shoal 
of  meteoric  particles,  vaporized  in  their  passage  through 
space,  under  conditions  not  yet  fully  understood.  The 
practical  identity  of  composition  between  comets  and 
meteors  had  long  been  suspected,  but  it  was  not  com- 
pletely confirmed  until  2/th  November,  1885,  when  mete- 
orites which  fell  to  the  earth  from  a  shower  of  Bielids  were 
picked  up  in  Mexico,  and  chemical  and  physical  investiga- 
tion established  their  undoubted  nature  as  originally  part 
of  the  lost  Biela's  comet. 

Falls  of  Meteorites.  —  In  general  the  meteorites  are 
divided  into  two  classes :  meteoric  stones  and  meteoric 
irons.  Falls  of  the  stony  meteorites  have  been  much 
oftener  seen  than  actual  descents  of  masses  of  meteoric 
iron.  The  most  remarkable  fall  ever  seen  took  place  on 
loth  May,  1879,  m  Iowa,  the  heaviest  stone  weighing  437 
pounds.  This  is  two  thirds  the  weight  of  the  largest 
meteoric  stone  ever  discovered,  though  not  actually  seen 
to  fall.  It  was  found  in  Hungary  in  1866,  and  is  now  part 
of  the  Vienna  collection.  The  iron  masses  are  often  much 
heavier:  the  ' signet'  meteorite,  a  complete  ring  found  in 
Tucson,  Arizona,  and  now  in  the  United  States  National 
Museum  at  Washington,  weighs  1400  pounds ;  a  Texas 
meteorite,  now  part  of  the  Yale  collection,  weighs  1635 
pounds ;  and  a  Colorado  meteorite  in  the  Amherst  collec- 
tion weighs  437  pounds.  But  although  the  cabinets  con- 
tain hundreds  of  specimens  of  meteoric  irons,  only  eight  or 
ten  have  actually  been  seen  to  fall. 


Analysis  of  Meteorites 


419 


Of  these,  the  largest  one  fell  in  Arabia  in  1865,  and  its  weight  is  130 
pounds.  It  is  now  in  the  British  Museum.  The  average  velocity  of 
meteors  is  35  miles  per  second.  Their  visibility  begins  at  an  altitude 
of  about  70  miles,  and  they  fade  out  at  half  that  height.  The  work 
done  by  the  atmosphere  in  suddenly  checking  their  velocity  appears  in 
large  part  as  heat  which  fuses  the  exterior  to  incandescence,  and  leaves 
them,  when  cooled,  thinly  encrusted  as  if  with  a  dense  black  varnish. 
The  iron  meteorites,  not  reduced  by  rust,  are  invariably  covered  with 
deep  pittings  or  thumb  marks.  Meteorites  are  always  irregular  in  form, 
never  spherical ;  and  the  pittings  are  in  part  due  to  impact  of  minute 
aerial  columns  which  resist  their  swift  passage  through  the  air. 

Analysis  of  the  Meteorites.  —  Meteoric  iron  is  an  alloy, 
containing  on  the  average  ten  per  cent  of  nickel,  com- 
mingled with  a  much  smaller  amount 
of  cobalt,  copper,  tin,  carbon,  and  a 
few  other  elements.  Meteoric  iron 
is  distinguishable  from  terrestrial 
irons  by  means  of  the  'Widmann- 
stattian  figures,'  which  etch  them- 
selves with  acids  upon  the  polished 
metallic  surface  —  a  test  which  rarely 
fails.  The  illustration  shows  these 
figures  of  their  true  size,  as  it  was 
made  from  a  transfer  print  from  the 
actual  etched  surface  of  a  meteorite 
in  the  Amherst  collection.  In  me- 
teoric stones,  chemical  analysis  has  revealed  the  pres- 
ence of  about  one  third  of  all  the  elemental  substances 
recognized  in  the  earth's  crust ;  among  them  the  elements 
found  in  meteoric  irons,  also  sulphur,  calcium,  chlorine, 
sodium,  and  many  others. 

The  minerals  found  in  meteoric  stones  are  those  which  abound  in 
terrestrial  rocks  of  igneous  or  volcanic  origin,  like  traps  and  lavas. 
Carbon  sometimes  is  found  in  meteorites  as  diamond.  The  analysis 
of  meteorites  has  brought  to  light  a  few  compounds  new  to  mineralogy, 
but  has  not  yet  led  to  the  discovery  of  any  new  element ;  and  the  study 


Widmannstattian  Figures 


420  Comets  and  Meteors 

of  meteorites  is  now  the  province  of  the  crystallographer,  the  chemist, 
and  the  mineralogist,  rather  than  the  astronomer.  Even  the  most 
searching  investigation  has  so  far  failed  to  detect  any  trace  of  organic 
life  in  meteorites. 

Occlusion  is  the  well-known  property  of  a  metal,  par- 
ticularly iron,  by  which  at  high  temperatures  it  absorbs 
gases,  and  retains  them  until  again  heated  red  hot.  Hy- 
drogen, carbonic  oxide,  and  nitrogen  are  usually  present  in 
iron  meteorites  as  occluded  gases,  also,  in  very  small  quan- 
tities, the  light  gas,  newly  discovered,  called  helium.  In 
1867,  during  a  lecture  on  meteors  by  Graham,  a  room 
in  the  Royal  Institution,  London,  was  lighted  by  gas 
brought  to  earth  in  a  meteorite  from  interplanetary  space. 
We  have  now  traversed  the  round  of  the  solar  system  ;  it 
remains  only  to  consider  the  bodies  of  the  sidereal  system, 
and  the  views  held  by  philosophers  concerning  the  pro- 
gressive development  of  the  material  universe. 


CHAPTER   XVI 

THE  STARS   AND  THE  COSMOGONY 

OUR  descriptions  of  heavenly  bodies  thus  far  have  con- 
cerned chiefly  those  belonging  to  the  solar  system. 
We  found  distance  growing  vast  beyond  the  power 
of  human  conception,  as  we  contemplated,  first  the  neigh- 
borly moon,  then  the  central  orb  of  the  system  400  times 
farther  away,  and  finally  Neptune,  30  times  farther  than 
the  sun,  —  not  to  say  some  of  the  comets  whose  paths 
take  them  even  remoter  still.  But  outside  of  the  solar 
system,  and  everywhere  surrounding  it,  is  a  stellar  universe 
the  number  of  whose  countless  hosts  is  in  some  sense  a 
measure  of  their  inconceivable  distance  from  our  humble 
abode  in  space. 

The  Sidereal  System. — All  these  bodies  constitute  the 
sidereal  system,  or  the  stellar  universe.  It  comprises  stars 
and  nebulae ;  not  only  those  which  are  visible  to  the  naked 
eye,  but  hundreds  of  thousands  besides,  so  faint  that  their 
existence  is  revealed  only  by  the  greatest  telescopes  and 
the  most  sensitive  photographic  plates.  Remoteness  of 
the  stars  at  once  forbids  supposition  that  they  are  similar 
in  constitution  to  planets,  shining  by  light  reflected  from 
the  sun  as  the  moon  and  planets  do.  Even  Neptune,  on  the 
barriers  of  our  system,  is  too  faint  for  the  naked  eye  to 
grasp  his  light.  But  the  nearest  fixed  star  is  about  9000 
times  more  distant.  So  the  very  brightness  of  the  lucid 
stars  leads  us  to  suspect  that  they  at  least  must  be  self- 
luminous  like  the  sun ;  and  when  their  light  is  analyzed 

421 


422 


Stars  and  Cosmogony 


with  the  spectroscope,  the  theory  that  they  are  suns  is 
actually  demonstrated.  It  is  reasonable  to  conclude,  then, 
that  the  sun  himself  is  really  a  star,  whose  effulgence,  and 
importance  to  us  dwellers  on  the  earth,  are  due  merely  to 
his  proximity.  The  figure  below  will  help  this  conception : 
for  if  we  recede  from  the  sun  even  as  far  as  Neptune,  his 
disk  will  have  shrunk  almost  to  a  point,  though  a  dazzling 
one.  Were  this  journey  to  be  continued  to  the  nearest 
star,  our  sun  would  have  dwindled  to  the  insignificance 
of  an  ordinary  star. 

The  Magnitudes  of  Stars.  —  While  stars  as  faint  as  the 
sixth  magnitude  can  just  be  seen  by  the  ordinary  eye  on 

a  clear  dark  night,  still 
other  and  fainter  stars  can 
be  followed  with  the  tele- 
scope far  beyond  this 
limit,  to  the  fifteenth  mag- 
nitude and  even  farther 
by  the  largest  instruments. 
Division  into  magnitudes, 
although  made  arbitrarily, 
is  a  classification  war- 
ranted by  time,  and  use 
of  many  generations  of 
astronomers.  Brightness 
of  stars  decreases  in  geo- 
metric proportion  as  the 
number  indicating  magni- 
tude increases ;  the  con- 
stant term  being  2\.  Thus, 
an  average  star  of  the  first  magnitude  is  2\  times  brighter 
than  one  of  the  second  magnitude ;  a  second  magnitude 
star  gives  2\  times  more  light  than  one  of  the  third  magni- 
tude, and  so  on.  At  the  observatory  of  Harvard  College, 


APPARENT 

SIZE   OF 

THE  SUN 

A  5  SEEN  FROM 

MERCURY 


Our  Sun  but  a  Brilliant  Star  as  seen  from 
Neptune 


The  Brightest  Stars 


423 


Pickering,  its  director,  has  devoted  many  years  to  determi- 
nation of  stellar  magnitudes  with  the  meridian  photometer, 
a  highly  accurate  instrument  of  his  devising,  by  which 
the  brightness  of  any  star  at  culmination  may  be  compared 
directly  with  Polaris  as  a  standard.  Brightest  of  all  the 
stars  is  Sirius,  and  as  no  others  are  so  brilliant,  strictly 
he  ought  perhaps  to  be  the  only  first  magnitude  star.  But 
many  fainter  than  Sirius  are  ranked  in  this  class,  three 
of  them  so  bright  that  their  stellar  magnitude  is  negative, 
as  below.  Decimal  fractions  express  all  gradations  of 
magnitude.  Even  the  surpassing  brilliancy  of  the  sun 
can  be  indicated  on  the  same  scale;  the  number—  25.4 
expresses  his  stellar  magnitude. 

The  Brightest  Stars.  —  Twenty  stars  are  rated  of  the 
first  magnitude;  half  of  them  are  in  the  northern  hemi- 
sphere of  the  sky.  They  are  the  following :  — 

THE  BRIGHTEST  STARS 


ORDER 

STELLAR 

ORDER 

STELLAR 

BRIGHT- 

MAG- 

STARS' NAMES 

BRIGHT- 

MAG- 

STARS' NAMES 

NESS 

NITUDE 

NESS 

NITUDE 

I 

-1.4 

a  Canis  Majoris  (Sirius) 

II 

0.9 

a  Orionis  (Betelgeux) 

2 

-0.8 

o-  Argils  (  Canopus)  * 

12 

0.9 

a  Crucis  * 

3 

—O.I 

a.  Centauri  * 

13 

0.9 

aAquilae  (Altair) 

4 

O.I 

a  Aurigae  (  Capella) 

14 

I.O 

aTauri  (Aldebarari) 

5 

O.2 

aBootis  (Arcturus) 

IS 

i.i 

a.  Virginis  (Spica) 

6 

0.2 

a  Lyrae  (  Vega) 

16 

1.2 

aScorpii  (Antares) 

7 

°-3 

POrionis  (Rigel) 

17 

1.2 

£  Geminorum  (Pollux) 

8 

0.4 

a  Eridani  (Achernar)  * 

18 

i-3 

a  Piscis  Australis 

9 

0.5 

a  Canis  Minoris 

(Fomalhauf) 

(Procyori) 

19 

i-3 

aLeonis  (Regulus) 

10 

0.7 

/3  Centauri  * 

20 

1.4 

aCygni  (Deneb) 

These    stars   culminate   at    different   altitudes   varying 
with  their  declination,  and  at  different  times  throughout 

*  Invisible  in  our  middle  northern  latitudes. 


424  Stars  and  Cosmogony 

the  year,  which  you  may  find  from  charts  of  the  constella- 
tions (pp.  60-63). 

Number  of  the  Stars.  —  Besides  twenty  stars  of  the  first 
magnitude,  not  only  are  there  nearly  six  thousand  of 
lesser  magnitude  visible  to  the  naked  eye,  likewise  many 
hundreds  of  thousands  visible  in  telescopes  of  medium 
size,  but  also  millions  of  stars  revealed  by  the  largest 
telescopes.  From  careful  counts,  partly  by  Gould,  the 
number  of  stars  of  successive  magnitudes  is  found  to  in- 
crease nearly  in  geometric  proportion  :  — 

ist  magnitude     20  6th  magnitude  5000 

2d          "             65  7th          "  20,000 

3d          "            200  8th          "  68,000 

4th         "            500  9th          "  240,000 

5th         "           1400  loth         "  720,000 

Any  glass  of  two  inches  aperture  should  show  all  these 
stars.  But  in  order  to  discern  all  the  uncounted  millions 
of  yet  fainter  stars,  we  need  the  largest  instruments,  like 
the  Lick  and  the  Yerkes  telescopes.  Their  approximate 
number  has  been  ascertained  not  by  actual  count,  but 
by  estimates  based  on  counts  of  typical  areas  scattered 
in  different  parts  of  the  heavens.  The  number  of  stars 
within  reach  of  our  present  telescopes  perhaps  exceeds 
125  millions.  But  the  telescope  by  itself,  no  matter 
how  powerful,  is  unable  to  detect  any  important  difference 
between  these  faint  and  multitudinous  luminaries ;  seem- 
ingly all  are  more  alike  than  peas  or  rice  grains  to  the 
naked  eye.  There  is  good  reason  for  believing  that  the 
dark  or  non-luminous  stars  are  many  times  more  numerous 
than  the  visible  ones,  and  modern  research  has  made  the 
existence  of  many  such  invisible  bodies  certain. 

Total  Light  from  the  Stars.  —  Argelander,  a  distin- 
guished German  astronomer,  made  a  catalogue  and  chart 
of  all  the  stars  of  the  northern  hemisphere  increased  by 


Colors  of  the  Stars  425 

an  equatorial  belt,  one  degree  in  width,  of  the  southern 
stars.  His  limit  was  the  Q|-  magnitude,  and  he  recorded 
rather  more  than  324,000  stars  in  all.  Accepting  a  sixth 
magnitude  star  as  the  standard,  and  expressing  in  terms  of 
it  the  light  of  all  the  lucid  stars  registered  by  Argelander, 
they  give  an  amount  of  light  equivalent  to  7300  sixth 
magnitude  stars.  But  calculation  proves  also  that  the 
telescopic  stars  of  this  extensive  catalogue  yield  more  than 
three  times  as  much  light  as  the  lucid  ones  do.  The  stars, 
then,  we  cannot  see  with  the  naked  eye  give  more  light 
than  those  we  can,  because  of  their  vastly  greater  num- 
bers. If,  now,  we  suppose  the  southern  heavens  to  be 
studded  just  as  thickly  as  the  northern,  there  would  be  in 
the  entire  sidereal  heavens  about  600,000  stars  to  the 
9|  magnitude ;  and  their  total  light  has  been  calculated 
equal  to  -fa  that  of  the  average  full  moon. 

Colors  of  the  Stars.  —  A  marked  difference  in  color  characterizes 
many  of  the  stars.  For  example,  the  polestar  and  Procyon  are  white, 
Betelgeux  and  Antares  red,  Capella  and  Alpha  Ceti  yellowish,  Vega 
and  Sirius  blue.  Among  the  telescopic  stars  are  many  of  a  deep  blood- 
red  hue;  variable  stars  are  numerous  among  these.  In  observing  true 
stellar  colors,  the  objects  should  be  high  above  the  horizon,  for  the 
greater  thickness  of  atmosphere  at  low  altitudes  absorbs  abundantly  the 
bluish  rays,  and  tends  to  give  all  stars  more  of  an  orange  tint  than  they 
really  possess.  Colors  are  easier  to  detect  in  the  case  of  double  stars 
(page  451%  because  the  components  of  many  of  these  objects  exhibit 
complementary  colors  ;  that  is,  colors  which  produce  white  light  when 
combined.  If  components  of  a  «  double1  are  of  about  the  same  magni- 
tude, their  color  is  usually  the  same ;  if  the  compinion  is  much  fainter, 
its  color  is  often  of  complementary  tint,  and  always  nearer  the  blue  end 
of  the  spectrum.  Complementnry  colors  are  better  seen  with  the  stars 
out  of  focus.  Following  are  a  few  of  these  colored  double  stars  :  — 

77  Cassiopeiae.     yellow  and  purple,  4  mag.       J\  mag- 

y  Andromedae,  orange  and  green,  3}  5^. 

i  Cancri,  orange  and  blue,  4?  6 

a  Herculis,         orange  and  green,  3  6 

ft  Cygni,  yellow  and  blue,  3  7 


426  Stars  and  Cosmogony 

There  is  some  evidence  that  a  few  stars  vary  in  color  in  long  periods 
of  time ;  for  example,  two  thousand  years  ago  Sirius  was  a  red  star, 
now  it  is  bluish  white.  Any  significance  of  color  as  to  age  or  intensity 
of  heat  is  not  yet  recognized ;  rather  is  it  probably  due  to  variant  com- 
position of  stellar  atmospheres. 


Star  Catalogues  and  Charts.  —  When  you  consult  a 
gazetteer  you  find  a  multitude  of  cities  set  down  by  name. 
Corresponding  to  each  is  its  latitude,  or  distance  from 
the  equator,  and  its  longitude,  or  arc  distance  on  the 
equator,  measured  from  a  departure  point  or  prime  merid- 
ian. These  arcs  are  measured  on  the  surface  of  our 
earth.  Turning,  then,  to  the  map,  you  find  the  city  in 
question,  and  perhaps  many  neighboring  ones  set  down  in 
exact  relation  to  it.  Precisely  in  a  similar  manner  all  the 
brighter  stars  of  the  sky  are  registered  in  their  true  rela- 
tions one  to  another,  on  charts  and  photographic  plates. 
These  will  be  accurate  enough  for  many  purposes,  but  not 
for  all.  When  a  higher  precision  is  required,  one  must 
consult  those  gazetteers  of  the  sky  known  as  star  cata- 
logues. Set  down  in  them  will  be  found  the  coordinates 
of  a  star ;  that  is,  its  right  ascension  and  declination,  the 
counterparts  of  terrestrial  longitude  and  latitude.  But  we 
shall  soon  observe  this  peculiar  difference  between  longitude 
on  the  earth  and  right  ascension  in  the  sky  :  the  star's  right 
ascension  will  (in  nearly  all  cases)  be  perpetually  increas- 
ing, while  the  longitude  of  a  place  remains  always  the 
same.  This  perpetual  shifting  of  the  stars  in  right  ascen- 
sion is  mostly  due  to  precession.  It  is  as  if  Greenwich  or 
Washington  were  constantly  traveling  westward,  but  so 
slowly  that  only  in  26,000  years  would  it  have  traveled  all 
the  way  round  the  globe. 

Precession  and  Standard  Catalogues.  —  It  was  Hipparchus 
(B.C.  130)  who  first  discovered  this  perpetual  and  apparent 
shifting  of  all  the  stars.  And  partly  for  this  reason  he 


Photographic  Charts  of  the  Heavens       427 

made  a  catalogue  (the  first  one  ever  constructed)  of  1080 
stars,  so  that  the  astronomers  coming  after  him  might,  by 
comparing  his  map  and  catalogue  with  their  own,  dis- 
cover what  changes,  if  any,  are  in  progress  among  the 
stellar  hosts.  No  competitor  appeared  in  the  field,  until 
the  1 5th  century,  when  the  second  catalogue  was  con- 
structed, by  Ulugh-Beg  (A.D.  1420),  an  Arabian  astrono- 
mer. Since  his  day  vast  improvements  have  been  made 
in  methods  of  observing  the  stars,  and  in  calculating 
observations  of  them.  There  are  now  about  100  large 
catalogues  of  stars,  constructed  by  astronomers  of  both 
hemispheres ;  and  the  place  of  every  star  in  the  entire 
celestial  sphere  revealed  by  telescopes  of  medium  dimen- 
sion will  soon  be  determined  with  astronomical  precision. 
Several  of  the  larger  government  observatories  prepare  a 
catalogue  of  stars  every  year  from  their  observations ;  and 
these  again  are  combined  into  other  and  more  accurate 
catalogues  (called  standard  catalogues),  especially  of  the 
zodiacal  stars.  These  afford  average  or  mean  positions  of 
stars  for  the  beginning  of  a  particular  year,  called  the 
epoch  of  the  catalogue.  Positions  for  any  given  dates  are 
obtained  by  bringing  the  epoch  forward,  and  farther  cor- 
recting for  precession,  aberration,  and  nutation  (pages  1 30, 
164,  and  390).  The  mean  position  so  corrected  becomes 
the  apparent  place.  The  chief  American  authorities  on 
standard  stellar  positions  are  Newcomb,  Boss,  and  Safford. 

Photographic  Charts  of  the  Entire  Heavens.  —  On  proposal  of  David 
Gill,  her  Majesty's  astronomer  at  the  Cape  of  Good  Hope,  an  inter- 
national congress  of  astronomers  met  at  Paris  in  1887,  and  arranged  for 
the  construction  of  a  photographic  chart  of  the  entire  heavens.  The 
work  of  making  the  charts  has  been  allotted  to  18  observatories,  one 
third  of  which  are  located  in  the  southern  hemisphere.  They  are 
equipped  with  1 3-inch  telescopes,  all  essentially  alike;  and  exposures 
are  of  such  length  as  to  include  all  stars  to  the  I4th  magnitude,  prob- 
ably more  than  50  millions  in  all.  Stars  to  the  I  ith  magnitude  inclusive 
(about  2,000,000)  are  to  be  counted  and  their  positions  measured  and 


%    ".*• 

Jf       •  • 


f  '.  «'• 


VfTt^ 

•^  ; 


IA  .:.•»••"'•  :• 

The  Vicinity  of  i?  Carinae  (Eta  Argus),  /R  10  h.  41  m.,  Decl.  S-  59°  (photographed  by 
Bailey  with  the  Bruce  Telescope,  1896.     Exposure  4  hours) 

428 


Proper  Motions  of  the  Stars  429 

catalogued.  Each  photograph  covers  an  area  of  four  square  degrees  ; 
and  as  duplicate  exposures  are  necessary,  the  total  number  of  plates 
will  be  not  less  than  25,000.  The  entire  expense  of  this  comprehensive 
map  of  the  stars  will  exceed  $2,000,000.  The  observatories  of  the 
United  States  have  taken  no  part  in  this  cooperative  programme ;  but 
by  the  liberality  of  Miss  Bruce,  the  Observatory  of  Harvard  College, 
which  has  a  station  in  Peru  also,  has  undertaken  independently  to  chart 
in  detail  the  more  interesting  regions  of  the  entire  heavens,  with  the 
Bruce  photographic  telescope,  a  photographer's  doublet  consisting  of 
four  lenses,  each  24  inches  in  aperture.  A  section  of  a  recent  chart 
obtained  with  this  great  instrument  is  shown  opposite.  The  plates  are 
14  x  17  inches  ;  about  two  thousand  will  be  required  to  cover  the  entire 
sky.  On  the  original  plate  of  which  the  illustration  is  part  were  counted 
no  less  than  400,000  stars.  Also  Kapteyn  has  measured  and  catalogued 
about  300,000  stars  on  plates  taken  at  Capetown. 

Proper  Motions  of  the  Stars.  —  If  Ptolemy  or  Kepler 
or  any  great  astronomer  of  the  past  were  alive  to-day, 
and  could  look  at  the  stars  and  constellations  as  he  did  in 
his  own  time,  he  would  be  able  to  discern  no  change  what- 
ever in  either  the  brightness  of  the  stars  or  their  apparent 
positions  relatively  to  each  other.  Consequently  they  seem 
to  have  been  well  named  fixed  stars.  If,  however,  we  com- 
pare closely  the  right  ascensions  and  declinations  of  stars 
a  century  and  a  half  ago  with  their  corresponding  positions 
at  the  present  day,  we  find  that  very  great  changes  are 
taking  place  ;  but  these  changes  relatively  to  the  imaginary 
circles  of  the  celestial  sphere  are  in  the  main  due  to  pre- 
cessional  motion  of  the  equinox.  A  star's  annual  proper 
motion  in  right  ascension  is  the  amount  of  residual  change 
in  its  right  ascension  in  one  year,  after  allowance  for  aber- 
ration, and  motion  of  the  equinox.  The  proper  motion  in 
declination  may  be  similarly  defined.  Proper  motion  is 
simply  an  angular  change  in  position  athwart  the  line  of 
vision,  and  may  correspond  to  only  a  small  fraction  of  the 
star's  real  motion  in  space. 

As  a  whole,  proper  motion  of  the  brighter  stars  exceeds  that  of 
the  fainter  ones,  because  they  are  nearer  to  us ;  and  proper  motion  is  a 


430 


Stars  and  Cosmogony 


combined  effect  of  the  sun's  motion  in  space  and  of  the  stars  among 
each  other.     Ultimately  these  two  effects  can  be  distinguished.     Still, 

even  the  largest  proper  mo- 
tion yet  known,  that  of  a  star 
in  Ursa  Major,  No.  1830  in 
Groombridge's  catalogue,  and 
often  called  the  '  runaway 
star,' is  only  7". 6;  and  nearly 
three  centuries  must  elapse 
before  it  would  seem  to  be 
displaced  so  much  as  the 
breadth  of  the  moon.  The 
average  proper  motion  of 
first  magnitude  stars  is  about 
o".25 ;  and  of  sixth  magni- 
tude stars,  only  one  sixth 
Ursa  Major  now,  and  after  400  Centuries  as  great.  Among  European 

astronomers  Auwers  has  con- 
tributed most  to  these  critical  studies,  and  Porter  in  America  has 
published  a  catalogue  of  proper  motions. 

Secular  Changes  in  the  Constellations.  —  The  accumu- 
lated proper  motion  of  the  stars  of  a  given  asterism  will 
hardly  change  its  naked-eye  appearance  appreciably  within 
2000  years.  But  when  intervals  of  1 5  to  20  times  greater 
are  taken,  the  present  well-known  constellation  figures 
will  in  many  cases  be  seriously  distorted. 

Particularly  is  this  true  of  Cassiopeia,  Orion,  and  Ursa  Major.  In 
the  left-hand  diagram  above  is  shown  the  present  asterism  of  the  Dipper, 
to  each  star  of  which  is  attached  an  arrow  indicating  the  direction  and 
amount  of  its  proper  motion  in  about  400  centuries.  The  companion 
diagram  at  the  right  is  a  figure  of  the  same  constellation  (according 
to  Proctor)  after  that  interval  has  elapsed :  though  much  distorted,  it 
would  be  recognized  as  Ursa  Major  still.  As  indicated  by  the  direction 
of  the  arrows,  the  extreme  stars,  Alpha  and  Eta,  seem  to  move  almost 
in  the  opposite  direction  from  the  others,  and  observations  with  the 
spectroscope  confirm  this  result.  As  the  spectra  of  the  five  intermediate 
stars  are  quite  identical,  it  is  likely  that  they  originally  formed  part  of 
a  physically  connected  system.  Most  of  the  brighter  stars  of  the 
Pleiades  are  also  moving  in  one  and  the  same  direction,  and  this  com- 
munity of  proper  motion  has  received  the  name  star  drift. 


Apex  of  the  Suns   Way  431 

Apex  of  the  Sun's  Way.  —  When  riding  upon  the  rear 
platform  of  a  suburban  electric  car,  where  the  ties  are  not 
covered  under,  observe  that  they  seem  to  crowd  rapidly 
together  as  the  car  swiftly  recedes  from  them.  If  possible 
to  watch  from  the  front  platform,  precisely  the  opposite 
effect  will  be  noticed :  the  ties  seem  to  open  out  and  sepa- 
rate from  each  other  just  as  rapidly.  In  like  manner 
the  stars  in  one  part  of  the  celestial  sphere,  when  taken  by 
thousands,  are  found  to  have  a  common  element  of  proper 
motion  inward  toward  a  center  or  pole ;  while  in  the 
opposite  region,  they  seem  to  be  moving  radially  out- 
ward, as  if  from  the  hub  and  along  the  spokes  of  a  wheel. 
This  double  phenomenon  is  explained  by  a  secular  motion 
of  the  sun  through  space,  transporting  his  entire  family  of 
planets,  satellites,  and  comets  along  with  him.  This  hub 
or  pole  toward  which  the 
solar  system  is  moving  is 
called  the  sun  s  goal,  or  the 
apex  of  the  suns  way ;  and 
recent  determinations  by  L. 
Struve,  Boss,  and  Porter 
make  it  practically  coinci- 
dent with  the  star  Vega. 
Similarly  the  point  from 
which  we  are  receding  is 

Earth's  Helical  Path  in  Space 

known    as    the    sun's   quit, 

and  it  is  roughly  a  point  halfway  between  Sirius  and 
Canopus.  So  vast  is  this  orbit  of  the  sun  that  no  deviation 
from  a  straight  line  is  yet  ascertained,  although  our  motion 
along  that  orbit  is  about  12  miles  every  second. 

This  result  is  verified  both  by  discussion  of  proper  motions,  and 
by  finding  the  relative  movement  of  stars  '  fore  and  aft '  by  means  of 
the  spectroscope.  As  yet,  however,  there  is  no  indication  of  a  <  central 
sun,'  a  favorite  hypothesis  in  the  middle  of  the  iQth  century.  This 


432  Stars  and  Cosmogony 

motion  of  the  sun  does  not  interfere  with  the  relations  of  his  family 
of  planets  to  him  ;  but  simply  makes  them  describe,  as  in  the  figure 
just  given,  vast  spiral  circumvolutions  through  interstellar  space. 

Stellar  Motions  in  the  Line  of  Sight.  —  From  a  bridge 
spanning  a  rivulet,  whose  current  is  uniform,  we  observe 
chips  floating  by,  one  every  15  seconds.  Ascending  the 
stream,  we  find  their  origin :  an  arithmetical  youth  on  the 
bank  has  been  throwing  them  into  mid-stream  at  regular 
intervals,  four  chips  to  the  minute.  We  interfere  with  his 
programme  only  by  asking  him  first  to  walk  down  stream 
for  two  minutes,  then  to  return  at  the  same  uniform  speed ; 
and  to  repeat  this  process  several  times,  always  taking 
care  to  throw  the  chips  at  precisely  the  same  intervals  as 
before.  Returning  to  the  bridge  to  observe,  we  find  the 
chips  no  longer  pass  at  intervals  of  1 5  seconds  as  at  first ; 
but  that  the  interval  is  less  than  this  amount  while  the 
boy  who  tosses  them  is  walking  down  stream,  and  greater 
by  a  corresponding  amount  while  he  is  going  in  the  oppo- 
site direction.  By  observing  the  deviation  from  15  sec- 
onds, the  speed  at  which  he  walks  can  be  found.  Similarly 
with  the  motions  of  stars  toward  or  from  the  earth ;  the 
boy  is  the  moving  star,  and  the  chips  are  the  crests  of 
light  waves  emanating  from  it.  When  the  star  is  coming 
nearer,  more  than  the  normal  number  of  waves  reach  us 
every  second,  and  a  given  line  in  the  star's  spectrum  is 
displaced  toward  the  violet.  Likewise  when  a  star  is 
receding,  the  same  line  deviates  toward  the  red.  This 
effect  was  first  recognized  in  1842  by  Doppler,  from  whom 
comes  the  name  '  Doppler's  principle.'  Research  of  this 
character  is  an  important  part  of  the  programme  at  Green- 
wich (opposite),  and  at  the  Yerkes  Observatory  (page  7). 

The  spectral  observation  is  an  exceedingly  delicate  one ;  but  by 
measuring  the  degree  of  displacement  of  stellar  lines,  as  compared  with 
the  same  lines  due  to  terrestrial  substances  artificially  vaporized,  the 
motions  of  about  100  stars  toward  or  from  the  solar  system  have  been 


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434 


Stars  and  Cosmogony 


ascertained.  The  limit  of  accuracy  is  two  or  three  kilometers  per 
second.  The  observed  motions  of  stais,  not  situated  at  the  poles  of 
the  ecliptic,  or  near  them,  require  a  correction  depending  on  the  earths 
orbital  motion  round  the  sun.  When  thus  modified,  the  motions  of 
few  stars  in  the  line  of  sight  exceed  40  kilometers  per  second. 

Motions  of  Individual  Stars.  —  Chiefly  by  Huggins  of 
London,  Maunder  at  Greenwich,  Vogel  at  Potsdam,  Ger- 
many, and  Keeler  and  Campbell  at  the  Lick  Observatory, 
have  these  researches  been  conducted.  Below  are  results 
for  a  few  stars  showing  best  accordance  :  — 

MOTIONS  IN  THE  LINE  OF  SIGHT 


STAR'S  NAME 

POSITION  FOR  190x5.0 

MOTION  PER  SECOND 
TOWARD  OR  FROM  THE  SuN 

R.  A. 

DECL. 

MILES 

KILOMETERS 

Alpha  Arietis  .  . 
Aldebaran  .  .  . 
Rie-el 

h.       m. 
2         2 

4    30 
5     10 

5     5° 
10     14 

13      20 

15      30 
19      46 

o          ' 

N.  22     59 
N.  16     18 
S.    8     19 

N.    7     23 

N.  20      21 

S.  10    38 

N.27      3 
N.    8     36 

-  "7 
+  31.1 
+  13-6 
+  17.6 
-25.1 
—  10.6 
+  20.3 
-23.9 

-  J9 

+  50 
+  22 
+  28 
-40 
-   17 

+  33 
-38 

Betelgeux  .  .  . 
Gamma  Leonis  .  . 
Spica 

Alpha  Coronae  .  . 
Altair  

These  are  a  tenth  part  of  all  successfully  ascertained. 
Spectrum  photography  has  contributed  greatly  to  the  con- 
venience and  accuracy  of  these  critical  observations. 

Relation  of  Brightness  to  Distance  of  the  Stars.  —  Were 
the  stars  all  of  the  same  real  size  and  brightness,  their 
apparent  magnitudes,  combined  with  their  direction  from 
us,  would  make  it  possible  to  state  their  precise  arrange- 
ment throughout  the  celestial  spaces.  But  all  assumptions 
of  this  character  are  unfounded,  and  lead  to  erroneous 
conclusions.  The  very  little  yet  known  about  the  real  dis- 


Stellar  Distances  435 

tances  of  the  stars  and  their  motions,  when  taken  in  con- 
nection with  their  apparent  magnitudes,  proves  conclusively 
that  many  of  the  fainter  stars  are  relatively  near  the  solar 
system ;  also  that  several  of  the  brighter  stars  are  exceed- 
ingly remote,  and  therefore  exceptionally  large  and  massive. 
Apparent  brightness,  therefore,  is  no  certain  criterion  of 
distance.  This  subject  of  investigation  is  so  vast  and 
intricate  that  very  little  headway  has  yet  been  securely 
made.  What  we  really  know  may  be  put  in  a  single  brief 
sentence :  Only  as  a  very  general  rule  is  it  true  that  the 
brighter  stars  are  nearer  and  larger  than  the  great  mass 
of  fainter  ones ;  and  to  this  rule  are  conspicuous  and  im- 
portant exceptions.  Our  knowledge  is  rather  negative  than 
positive;  and  we  may  be  certain  that  (i)  the  stars  are  far 
from  equally  distributed  throughout  space,  and  (2)  they 
are  far  from  alike  in  real  brightness  and  dimensions. 

How  Stellar  Distances  are  found.  —  Recall  the  instance  of 
the  earth  and  moon  (page  237) :  we  found  the  moon's  dis- 
tance from  us  by  measuring  her  displacement  among  the 
stars,  as  seen  from  two  observatories  at  the  ends  of  a  diam- 
eter of  our  globe,  or  as  near  its  extremities  as  convenient. 
But  this  earth  is  so  small,  that,  as  seen  from  a  star,  even  its 
entire  diameter  would  appear  as  an  infinitesimal ;  we  must 
therefore  seek  another  base  line.  Only  one  is  feasible ; 
and  although  25,000  times  greater,  still  it  is  hardly  long 
enough  to  be  practicable. 

Imagine  the  earth  replaced  by  a  huge  sphere,  whose  circle  equals 
our  orbit  round  the  sun.  From  the  ends  of  a  diameter,  where  we  are 
at  intervals  of  six  months,  we  may  measure  the  displacement  of  a  star, 
just  as  we  measured  the  displacement  of  the  moon  from  the  two  ob- 
servatories. We  find,  then,  that  half  this  displacement  represents  the 
star's  parallax,  just  as  half  the  moon's  displacement  gave  the  lunar 
parallax.  And  just  as  in  the  case  of  moon,  sun,  and  planets  we  em- 
ploy the  term  diurnal  parallax,  so  in  the  case  of  stars  we  call  annual 
parallax  the  angle  at  the  star  subtended  by  the  radius  of  earth's  orbit. 
Measurement  of  a  star's  annual  parallax  is  one  of  the  exceedingly  dim"- 


436 


Stars  and  Cosmogony 


cult  problems  that  confront  the  practical  astronomer;  so  small  is  the 
angle  that  its  measurement  is  much  as  if  a  prisoner  who  could  only  look 
out  of  the  window  of  his  cell  were  given  instruments  of  utmost  pre- 
cision and  compelled  to  as- 
certain  the    distance    of    a 
mountain  20  miles  away. 

A  Star's  Parallactic  El- 
lipse. —  Stand   a   book    on 
the  table,  and  place  the  eye 
about  two  feet  from  the  side 
//  of  it.     Hold  the  point  of  a 

pen  or  pencil  steadily,  at 
distances  of  about  5,  10, 
and  20  inches  from  the  eye, 
and  between  it  and  the 
book.  For  each  position  of 
the  pencil  move  the  head 
around  in  a  nearly  vertical 
circle  about  two  inches  in 
diameter,  noticing  in  each 
case  the  size  of  the  circle 
which  the  pen  point  appears 
to  describe  where  projected 
on  the  book.  This  con- 
clusion is  quickly  reached : 
the  farther  the  pencil  from 
the  eye,  the  smaller  this  cir- 
cle. Now  imagine  the  eye 
replaced  by  the  earth  in  its 
orbit  (as  at  the  bottom  of 
the  diagram),  the  pencil  by 
the  three  stars  shown,  and 
the  book  by  the  farthest 
stars.  Evidently  the  earth 
by  traveling  round  the  sun 
makes  the  stars  appear  to  de- 
scribe elliptic  orbits  whose 
size  is  precisely  proportioned  inversely  to  their  distance  from  the  solar 
system.  The  eccentricity  of  the  parallactic  ellipse  of  a  staY  is  exactly 
the  same  as  that  of  its  aberration  ellipse  already  figured  on  page  164: 
a  star  at  the  pole  of  the  ecliptic  describes  a  circle,  and  those  situated 
in  the  ecliptic  simply  oscillate  forth  and  back  in  a  straight  line.  Stars 
in  intermediate  latitudes  describe  ellipses  whose  eccentricities  are  de- 
pendent upon  their  latitude.  There  are  these  two  important  differ- 


'••HO  TH 


The  Nearest  Star  describes  the  Largest  Apparent 
Ellipse  among  the  Farthest  Stars 


Stellar  Distances 


437 


ences:  (i)  in  the  aberration  ellipse,  the  star  is  always  thrown  90° 
forward  of  its  true  position,  while  in  the  parallactic  ellipse,  it  is  just  180° 
displaced  ;  (2)  the  major  axis  of  the  aberration  ellipse  is  the  same  for 
all  stars,  but  in  the  parallactic  ellipse  its  length  varies  inversely  with 
the  distance  of  the  star.  Measurement  of  the  major  axis  of  this  ellipse 
affords  the  means  of  ascertaining  how  far  away  the  star  is,  because  the 
base  line  b  the  diameter  of  the  earth's  orbit.  This  is  called  the  differ- 
ential method,  because  it  determines,  not  the  star's  absolute  parallax, 
but  the  difference  between  its  parallax  and  that  of  the  remotest  star, 
assumed  to  be  zero.  Researches  on  stellar  distances  have  been  prose- 
cuted by  Gill  at  Capetown  and  Elkin  at  Yale  Observatory  with  a  high 
degree  of  accuracy  by  the  heliometer. 

The  Distance  of  61  Cygni.  —  The  star  known  as  61  Cygni  has 
become  famous,  because  it  is  the  first  star  whose  distance  was  ever 
measured.  This  great  step  in  our  knowledge  of  the  sidereal  universe 
was  taken  about  1840  by  the  eminent  German  astronomer  Bessel, 
often  called  the  father  of  practical  astronomy,  because  he  introduced 
many  far-reaching  improvements  conducing  to  higher  accuracy  in 
astronomical  methods  and  results.  This  star  is  a  double  star,  standing 
at  an  angle  with  the  hour  circle  (north-south),  as  the  diagram  shows. 
Two  small  stars  are  in  the  same  field  of  view,  a  and  b,  nearly  at  right 
angles  in  their  direction  from  the  double  star ;  and  Bessel  had  reason 
for  believing  that  they  were 
vastly  farther  away  than  61 
Cygni  itself.  So  at  opposite 
seasons  of  the  year  he  meas- 
ured with  the  heliometer  the 
distances  between  each  of 
the  components  of  61  Cygni 
and  both  the  stars  a  and  b. 
What  he  found  on  putting 
his  measures  together  was 
that  these  apparent  distances 
change  in  the  course  of  the 
year ;  and  that  the  nature  of 
the  change  was  exactly  what 
the  star's  position  relatively  to  the  ecliptic  led  him  to  expect.  The 
measured  amount  of  that  change,  then,  was  the  basis  of  calculation  of 
the  star's  distance  from  our  solar  system.  Within  recent  years  pho- 
tography has  been  successfully  applied  to  researches  of  this  character, 
with  many  advantages,  including  increased  accuracy  of  the  results, 
particularly  by  Pritchard. 

Illustration   of   Stellar    Distances.  —  The   nearest   of  all   the   fixed 
stars  is  Alpha  Centauri,  a  bright  star  of  the  southern  hemisphere.     Its 


Eessel's  Measures  of  Distance  of  61   Cygni 


438  Stars  and  Cosmogony 

parallax  is  ©".75,  and  it  is  275,000  times  more  distant  from  our  solar 
system  than  the  sun  is  from  the  earth.  But  there  is  little  advantage  in 
repeating  a  mere  statement  of  numbers  like  this.  Try  to  gain  some 
conception  of  its  meaning.  First,  imagine  the  entire  solar  system  as 
represented  by  a  tiny  circle  the  size  of  the  dot  over  this  letter  i. 
Even  the  sun  itself,  on  this  exceedingly  reduced  scale,  could  not  be 
detected  with  the  most  powerful  microscope  ever  made.  But  on  the 
same  scale  the  vast  circle  centered  at  the  sun  and  reaching  to  Alpha 
Centauri  would  be  represented  by  the  largest  circle  which  could  be  drawn 
on  the  floor  of  a  room  10  feet  square.  Or  the  relative  sizes  of  spheres 
may  afford  a  better  help.  Imagine  a  sphere  so  great  that  it  would 
include  the  orbits  of  all  the  planets  of  the  solar  system,  its  radius  being 
equal  to  Neptune's  distance  from  the  sun.  Think  of  the  earth  in  compari- 
son with  this  sphere.  Then  conceive  all  the  stars  of  the  firmament  as 
brought  to  the  distance  of  the  nearest  one,  and  set  in  the  surface  of  a 
sphere  whose  radius  is  equal  to  the  distance  of  that  star  from  us.  So 
vast  would  this  star  sphere  be  that  its  relation  to  the  sphere  inclosing 
the  solar  system  would  be  nearly  the  same  as  the  relation  of  this  latter 
sphere  to  the  earth.  When  studying  the  sun  and  the  large  planets,  it 
seemed  as  if  their  sizes  and  distances  were  inconceivably  great ;  but 
great  as  they  are,  even  the  solar  system  itself  is  as  a  mere  drop  to  the 
ocean,  when  compared  with  the  vastness  of  the  universe  of  stars. 

The  Unit  is  the  Light  Year.  —  In  expressing  intelligently 
and  conveniently  a  distance,  the  unit  must  not  be  taken  too 
many  times.  We  do  not  state  the  distance  between  New 
York  and  Chicago  in  inches,  or  even  feet,  but  in  miles. 
The  earth's  radius  is  a  convenient  unit  for  the  distance  of 
the  moon,  because  it  has  to  be  taken  only  60  times ;  but 
it  would  be  very  inconvenient  to  use  so  small  a  unit  in 
stating  the  distances  of  the  planets.  By  a  convention  of 
astronomers,  the  mean  radius  of  our  orbit  round  the  sun  is 
the  accepted  unit  of  measure  in  the  solar  system.  Simi- 
larly the  adopted  unit  of  stellar  distance  is,  not  the  distance 
of  any  planet  nor  the  distance  of  any  star,  but  the  distance 
traveled  by  a  light  wave  in  a  year.  This  unit  is  called 
the  light  year. 

The  velocity  of  light  is  186,300  miles  per  second,  and  it  travels  from 
the   sun  to  the   earth   in  499  seconds.     The  light  year  is  equal  to 


Distances  of  Well-known  Stars  439 

63,000  x  93,000,000  miles,  because  the  number  of  seconds  in  a  year  is 
about  499  x  63,000 ;  or,  the  light  year  is  equal  to  5  \  trillion  miles. 
Obviously,  as  stellar  parallax  has  a  definite  relation  to  distance,  parallax 
must  be  related  to  the  light  year  also :  the  distance  of  a  star  whose 
parallax  is  i"  is  about  3^  light  years.  So  that,  if  we  divide  3^  by  the 
parallax  (in  seconds  of  arc),  we  shall  have  the  star's  distance  in  light 
years. 

Distances  of  Well-known  Stars.  —  Although  the  paral- 
laxes of  more  than  a  hundred  stars  have  been  measured, 
only  about  50  are  regarded  as  well  known.  Twelve  are 
given  in  the  following  table,  together  with  their  corre- 
sponding distance  in  light  years:  — 


STELLAR  DISTANCES  AND  PARALLAXES 


M 

O 

APPROXIMATE 
[1900.0] 

DISTANCE  IN  — 

STAR'S  NAME 

1 

z 

PROPER 

MOTION 

PARAL- 
LAX 

< 

R.  A. 

DECL. 

LIGHT 
YEARS 

TRILLIONS 
OF  MILES 

h.    m 

0        ' 

.. 

., 

«  Centauri    .     .     . 

—  O.I 

H  33 

S.  60  25 

3.67 

o-75 

4* 

25 

61  Cygni  .... 

5-1 

21       2 

N.38  15 

5.I6 

0-45 

7i 

43 

Sinus       .... 

-1.4 

64I 

S.  16  35 

i-3« 

0.38 

H 

50 

Procyon  .... 

°-5 

7  34 

N.    5  29 

1.25 

0.27 

12 

71 

Altair  .... 

O  Q 

IQ   4.6 

N.   8  36 

o  6c 

O.2O 

16 

Q4 

o2  Eridani     .     .     . 

vy.y 

4.4 

*T?    Tv 

4     7 

S.    7     7 

tr.w^ 

4-°5 

0.19 

17 

-7*T 

IOO 

Groombridge  1830 

6.5 

ii     7 

N.  38  32 

7.65 

0.13 

25 

147 

Vega   . 

O.2 

18  34. 

N.  38  41 

0.36 

O.I  2 

27 

158 

Aldebaran     . 

1.0 

*•     JT- 

4  30 

AT  •     JV       if.  A 

N.  16  18 

V.JW 

0.19 

0.10 

"1 

32 

J 

191 

Capella    .... 

O.I 

5    9 

N.45  54 

0.43 

0.10 

32 

191 

Polaris     .     .     .     . 

2.1 

i  23 

N.  88  46 

0.05 

0.07 

47 

276 

Arcturus  .... 

0.2 

14  ii 

N.  19  41 

2.OO 

O.O2 

160 

950 

Most  of  these  are  bright  stars,  but  a  considerable  number 
of  faint  stars  have  large  parallaxes  also.  Relative  distances 
and  approximate  directions  from  the  solar  system  are  shown 
in  next  illustration,  for  a  few  of  the  nearer  and  best  deter- 


440 


Stars  and  Cosmogony 


mined  stars.  The  scale  is  necessarily  so  small  that  even 
the  vast  orbit  of  Neptune  has  no  appreciable  dimension. 
The  outer  circle  corresponds  nearly  to  a  parallax  o."i. 
The  distances  of  many  stars  have  been  ascertained  by 
Sir  Robert  Ball.  Various  determinations  often  differ 
widely. 


Distances  of  Stars  from  the  Solar  System  in  Light  Years  (according  to  Ranyard 
and  Gregory) 

Dimensions  of  the  Stars.  —  After  we  had  found  the  distance  of  the 
sun  and  measured  the  angle  filled  by  his  disk,  it  was  possible  to  calcu- 
late his  true  dimensions.  But  this  simple  method  is  inapplicable  to  the 
stars,  because  their  distances  are  so  vast  that  no  stellar  disk  subtends 
an  appreciable  angle.  Indirect  means  must  therefore  be  employed  to 
ascertain  their  sizes ;  and  it  cannot  be  said  that  any  method  has  yet 
yielded  very  satisfactory  results.  Combining  known  distance  with 
apparent  magnitude,  Maunder  has  calculated  the  absolute  light-giving 
power  of  the  following  stars,  that  of  the  sun  being  unity  :  — 


Types  of  Stellar  Spectra 


44 


SIRIAN  STARS 

Procyon 25 

Altair 25 

Sirius 40 

Regulus 1 10 

Vega 2050 


SOLAR  STARS 

Aldebaran 70 

Pollux 170 

Polaris 190 

Capella 220 

Arcturus    .                              .  6200 


But  these  are  far  from  indicating  their  real  magnitudes  ;  for  amount  of 
light  is  dependent  upon  intrinsic  brightness  of  the  radiating  surface, 
as  well  as  its  extent.  Among  the  giant  stars  are  Arcturus,  possibly  a 
hundredfold  the  sun's  diameter ;  also  Vega  and  Capella,  likewise  much 
larger  than  the  sun.  Algol,  too,  must  have  a  diameter  exceeding  a 
million  miles,  and  its  dark  companion  (page  450)  is  about  the  size  of 
the  sun — results  reached  by  means  of  the  spectroscope,  which  measures 
the  rate  of  approach  and  recession  of  Algol  when  the  invisible  attendant 
is  in  opposite  parts  of  its  orbit.  The  law  of  gravitation  gives  the  mass 
of  the  star  and  size  of  its  orbit,  so  that  the  length  of  the  eclipse  tells 
how  large  the  dark,  eclipsing  body  must  be. 

Types  of  Stellar  Spectra.  —  Sir  William  Huggins  in  1864 
first  detected  lines  indicating  the  vapor  of  hydrogen,  cal- 
cium, iron,  and  sodium  in  the  atmospheres  of  the  brighter 
stars.  Stellar  spectra  have  been  classified  in  a  variety  of 
ways,  but  the  division  into  four  types,  proposed  in  1865  by 
Secchi,  has  obtained  the  widest  adoption.  They  are  illus- 
trated on  the  next  page  :  — 

Type  I  is  chiefly  characterized  by  the  breadth  and  inten- 
sity of  dark  hydrogen  lines ;  also  a  decided  faintness  or 
entire  lack  of  metallic  lines.  Stars  of  this  type  are  very 
abundant.  They  are  blue  or  white  ;  Sirius,  Vega,  Altair, 
and  numerous  other  bright  stars  belong  to  this  type,  often 
called  Sirian  stars,  a  class  embracing  perhaps  more  than 
half  of  all  the  stars. 

Type  II  is  characterized  by  a  multitude  of  fine  dark,  me- 
tallic lines,  closely  resembling  the  solar  spectrum.  They  are 
yellowish  like  the  sun ;  Capella  and  Arcturus  (page  445) 
illustrate  this  type,  often  called  the  solar  stars,  which  are 
rather  less  numerous  than  the  Sirian  stars.  According  to 


442 


Stars  and  Cosmogony 


recent  results  of  Kapteyn,  absolute  luminous  power  of 
first  type  stars  exceeds  that  of  second  type  stars  seven- 
fold ;  and  stars  least  remote  from  the  sun  are  mostly  of 
the  second  type. 


Violet 


Red 


Type  II-    Capella  and  1he  Sun 


Type   III       Alpha   Htrculis 


Violet 


Type  IV  — I52  Schjellerup 
Secchi's  Four  Types  of  Stellar  Spectra 


Type  III  is  characterized  by  many  dark  bands,  well  de- 
nned on  the  side  toward  the  blue,  and  shading  off  toward 
the  red  end  of  the  spectrum  —  a  'colonnaded  spectrum,' 
as  Miss  Clerke  very  aptly  terms  it.  Orange  and  reddish 
stars,  and  a  majority  of  the  variables,  fall  into  this  cate- 
gory; Alpha  Herculis,  Mira,  and  Antares  are  examples  of 
this  type. 


Stellar  Spectrum  Photography  443 

Type  IV  is  characterized  by  dark  bands,  or  flutings  as 
they  are  often  technically  called,  similar  to  those  of  the 
previous  type,  only  reversed  as  to  shading  —  well  defined 
on  the  side  toward  the  red,  and  fading  out  toward  the  blue. 
Stars  of  this  type  are  few,  perhaps  50  in  number,  faint, 
and  nearly  all  blood-red  in  tint.  Their  atmospheres  con- 
tain carbon. 

Type  V  has  been  added  to  Secchi's  classification  by 
Pickering,  and  is  characterized  by  bright  lines.  From  two 
French  astronomers  who  first  investigated  objects  of  this 
class,  they  are  known  as  Wolf-Rayet  stars.  They  are  all 
near  the  middle  of  the  Galaxy,  and  their  number  is  about 
70.  They  are  a  type  of  stellar  objects  quite  apart  by 
themselves,  of  which  Campbell  has  made  an  especial 
study.  Many  objects  called  planetary  nebulae  yield  a 
spectrum  of  this  type. 

A  classification  by  Vogel  combines  Secchi's  types  III 
and  IV  into  a  single  type.  It  is  not  yet  determined 
whether  these  differences  of  spectra  are  due  to  different 
stages  of  development,  or  whether  they  indicate  real  differ- 
ences of  stellar  constitution.  Most  likely  they  are  due  to 
a  combination  of  these  causes. 

How  a  Star's  Spectrum  is  commonly  photographed.  —  The  light  of 
a  fixed  star  comes  to  the  earth  from  a  definite  point  on  the  dome  of  the 
sky,  so  that  a  stellar  image,  when  produced  by  the  object  glass  of  a 
telescope,  is  also  a  point.  Now  suppose  that  a  glass  prism  is  attached 
to  the  telescope  in  front  of  its  objective,  as  was  first  done  in  1824,  by 
Fraunhofer,  and  consider  what  takes  place ;  the  light  of  the  star  first 
passes  through  this  prism,  called  the  'objective  prism,'  and  then 
through  the  object  glass,  which  brings  the  rays  all  to  a  focus.  The 
star's  image,  however,  is  no  longer  a  point,  but  spread  out  into  a  line, 
made  up  of  many  colors  from  red  to  violet.  It  is  at  this  focus  that 
the  sensitive  dry  plate  is  inserted,  and  allowed  to  remain  until  the  ex- 
posure is  judged  sufficient  to  produce  the  desired  impression.  Perhaps 
three  hours  are  necessary ;  and  during  all  this  time  the  adjustment  of  the 
photographic  telescope  is  so  maintained  that  when  the  plate  is  de- 
veloped, the  spectra  of  all  the  stars  will  appear,  not  as  lines,  but  as  tiny 


444  Stars  and  Cosmogony 

rectangular  patches,  or  bits  of  ribbon  with  light  stripes  across  them.  A 
25th  part  of  such  a  negative  is  here  pictured,  as  obtained  with  the  Bache 

telescope  of  the  Boy  den  Observatory, 
by  exposure  in  1893  to  the  stars  of 
the  constellation  Carina.  On  it  were 
1000  spectra  sufficiently  distinct  for 
classification. 

The  Draper  Catalogue.  —  With 
an  identical  instrument,  similarly 
equipped  with  prisms,  stellar  spec- 
trum photography  has  been  vigo- 
rously conducted  at  Harvard  College 
Observatory  since  1886.  The  prisms 
are  mounted  with  their  edges  east 
and  west ;  and  the  clock  motion  is 
regulated  according  to  the  degree  of 
dispersion  employed,  as  well  as  the 
g  JML  •  •  magnitude  and  color  of  the  stars 

in  the    photographic  field.     Upon  a 
Spectra  of  Stars  in  Canna  (Pickering) 

(Exposure  2  h.  20m.)  single  plate  are  often  many  hundred 

spectra;    and  in  studying  them,  the 

great  advantage  of  such  close  juxtaposition  is  at  once  apparent.  For 
example,  the  spectra  of  about  50  stars  in  the  Pleiades  show  at  a 
glance  practical  identity  of  chemical  composition.  These  researches, 
conducted  under  the  superintendence  of  Edward  C.  Pickering,  at  the 
charges  of  a  fund  provided  by  Mrs.  Draper  as  a  memorial  to  her 
husband,  gave  to  astronomers  in  1890  the  'Draper  Catalogue  of  stellar 
spectra.1  including  more  than  10,000  stars  down  to  the  eighth  magnitude. 
Nearly  all  the  tedious  and  time-consuming  labor  of  examining  the 
plates  was  performed  by  Mrs.  Fleming,  Miss  Maury,  and  others.  This 
comprehensive  system  of  registering  spectra  naturally  paved  the  way 
for  a  more  detailed  classification  of  the  stars  than  Secchi's ;  and  with 
subsequent  work  at  the  same  observatory,  has  led  to  their  division  into 
about  20  groups.  Also  the  peculiarities  of  spectra  have  led  to  the 
detection  of  numerous  variable  stars,  and  several  new  or  temporary 
stars  (page  448) . 

Stellar  Spectra  of  High  Dispersion.  —  Vega  is  the  first  star  whose 
spectrum  was  successfully  photographed  by  Henry  Draper  in  1872. 
Brightest  stars  afford  sufficient  light  for  the  photography  of  their 
spectra,  even  after  a  high  degree  of  dispersion  by  a  train  of  several 
prisms,  or  by  a  diffraction  grating.  Multitudes  of  lines  are  thus  re- 
corded, especially  in  stars  of  the  solar  type.  A  part  of  the  photo- 
graphic spectrum  of  Arcturus  is  shown  on  next  page,  almost  a  duplicate 
of  the  solar  spectrum.  In  addition  to  the  fine  results  obtained  at 


Variable  Stars  445 

Cambridge  by  Pickering,  and  at  South  Kensington  by  Sir 
Norman  Lockyer,  must  be  mentioned  those  of  Vogel  and 
Scheiner  at  Potsdam,  near  Berlin ;  and  of  Deslandres  at 
Paris,  who  has  lately  detected  in  the  spectrum  of  Altair  a 
series  of  fine,  bright,  double  lines,  bisecting  the  dark  hydro- 
gen and  other  bands.  He  regards  them  as  indication  that 
this  star  is  enveloped  by  a  gaseous  medium  like  that  of  the 
solar  chromosphere. 

Variable  Stars,  -r-  A  star  whose  brightness  has 
been  observed  to  change  is  called  a  variable  star, 
or  simply  a  '  variable.'  Nearly  1000  such  objects 
are  now  recognized.  This  change  may  be  either 
an  increase  or  a  decrease ;  and  it  may  take  place 
either  regularly  or  irregularly.  Other  classes  of 
variables  rise  and  fall  in  different  ways  :  some  ex- 
hibiting several  fluctuations  of  brightness  in  every 
complete  period  (like  Beta  Lyrae,  a  well  known 
variable  whose  spectrum  presents  a  complexity 
of  hydrogen  lines  and  helium  bands  now  under 
investigation  by  Frost) ;  some  in  simple  periods 
only  a  few  hours  (the  shortest  at  present  known 
is  U  Pegasi,  5^  hours) ;  others  changing  slowly 
through  several  months.  In  general  the  last, 
which  are  usually  reddish  in  tint,  change  as 
rapidly  when  near  minimum  as  when  near  maxi- 
mum, their  light-curves  being  like  deep  waves 
with  sharp  crests.  Astronomers  term  these  'Omi- 
cron  Ceti  variables/  after  the  type  star  of  this 
name,  also  known  as  Mira,  or  'the  marvelous,' 
whose  variability  has  been  known  for  three  cen- 
turies. Their  average  period  is  about  a  year,  and 
perhaps  half  of  the  recognized  variables  are  of 
this  type.  Allied  to  them  are  the  temporary  stars 
described  in  a  subsequent  section.  Of  a  type 
whose  variation  is  the  reverse  of  Mira  are  the 


446 


Stars  and  Cosmogony 


'  Algol  variables,'  about  20  in  number,  whose  light  sud- 
denly drops  at  regular  intervals,  as  if  some  invisible  body 
were  temporarily  to  intervene. 

Knowledge  of  the  variable  stars  has  been  greatly  advanced  by  the 
labors  of  Chandler  and  Sawyer,  of  Cambridge.  Chandler's  catalogues 
contain  about  500  classified  variables.  Such  an  object,  previously  with- 
out a  name,  is  designated  by  letters  R,  S,  T,  U.  and  so  on,  in  order 
of  discovery  in  the  especial  constellation  where  found.  The  average 
range  in  recently  discovered  variables  is  less  than  one  magnitude. 

Distribution  and  Observation  of  Variables.  —  As  to  their  distribution 
over  the  heavens,  variable  stars  are  most  numerous  in  a  zone  inclined 
about  1 8°  to  the  celestial  equator,  and  split  in  two  near  where  the  cleft 
in  the  Galaxy  occurs.  Almost  all  the  temporary  stars  are  in  this  duplex 
region.  A  discovery  of  much  significance  was  made  by  Bailey,  in  1896, 
of  an  exceptional  number  of  variables  among  the  components  of  stellar 
clusters,  more  than  100  being  found  among  the  stars  of  a  single 
cluster;  and  the  mutations  of  magnitude  are  marked  within  a  few  hours. 
Variables  are  most  interesting  objects,  and  observations  of  great  value 
may  be  made  by  amateurs.  First  the  approximate  times  of  greatest  or 
least  brightness  must  be  ascertained ;  these  are  given  each  year  in  the 
*  Companion '  to  The  Observatory  (edited  by  Turner  and  published  at 
Greenwich),  and  in  Popular  Astronomy  (published  monthly  by  Payne 
at  Northfield,  Minnesota).  Following  are  a  few  variables,  easily  found 
from  star  charts  :  — 

VARIABLE  STARS 


POSITION  (1900  o) 

VARIATION 

STAR'S  NAME 

TYPE  OF 
VARIABLE 

R.  A. 

DECL. 

PERIOD 

RANGE 

h.          m. 

o        ' 

Days 

Magnitude 

Omicron  Ceti     . 

2          14 

S.     326 

331 

i.  7  to  9.5 

Mira. 

Beta  Persei    .     . 

3        2 

N.  40  34 

»i 

2.3  to  3  5 

Algol. 

Zeta  Geminorum 

6      58 

N.  20  43 

10} 

3.7  to  4.5 

R  Leonis  .     .     . 

9      42 

N.  ii  54 

313 

5.  2  to  10 

Delta  Librae  .     . 

14      56 

S.     8    7 

2} 

5  to  6.2 

Algol. 

Alpha  Herculis  . 

17       10 

N.  14  30 

90  ± 

3.1103.9 

Irregular. 

X  Sagittarii  . 

17      41 

S.  2748 

7 

4  to  6 

Beta  Lyrae     .     . 

18      46 

N.  33  15 

12.9 

3.4  to  4.5 

Delta  Cephei 

22         25 

N.  57  54 

5-s 

3.7  to  4-9 

Temporary,  or  New  Stars  447 

A  small  telescope  or  opera  glass  is  a  distinct  help  in  observing  a 
variable.  When  its  brightness  is  changing,  repeated  comparison  and 
careful  record  of  its  magnitude  with  that  of  .other  stars  in  the  same 
field,  will  make  it  possible  to  ascertain  the  time  of  maximum  or  mini- 
mum. Such  observations  are  of  use  to  the  professional  investigator  of 
periods  of  variable  stars. 

Temporary  Stars,  or  New  Stars.  —  A  variable  star  which, 
usually  in  a  few  weeks'  time,  vastly  increases  in  brightness, 
and  then  slowly  wanes  and  disappears  entirely,  or  nearly 
so,  is  called  a  temporary  star.  Accounts  of  several  such 
are  contained  in  ancient  historical  records.  In  the  Chinese 
annals  is  an  allusion  to  such  an  outburst  in  Scorpio,  B.C.  134; 
it  was  observed  by  Hipparchus,  and  led  to  his  construc- 
tion of  the  first  known  catalogue  of  stars,  made  with  refer- 
ence to  the  detection  of  similar  phenomena  in  the  future. 
Tycho  Brahe  carefully  observed  a  remarkable  object  of 
this  class  near  Cassiopeia,  which,  in  the  latter  part  of  1572, 
surpassed  the  brightness  of  Jupiter,  was  for  a  while  visible 
in  broad  daylight,  and,  in  a  year  and  a  half,  had  completely 
disappeared.  In  1604-5  a  new  star  °f  equal  brightness 
was  seen  by  Kepler  in  Ophiuchus  ;  it  also  disappeared. 
None  were  recorded  in  the  i8th  century.  Similar  and 
equally  remarkable  objects  made  their  appearance,  and 
passed  through  like  stages  near  our  own  day  in  — 

1866  in  Corona  Borealis  ; 

1876  in  Cygnus; 

1885  in  the  Great  Nebula  in  Andromeda; 

1891-92  in  Auriga. 

Such  a  star  is  often  called  Nova,  with  the  genitive  of  its 
constellation  added,  as  Nova  Cygni.  Temporary  stars 
remain  unchanged  in  apparent  position  during  their  great 
fluctuations  of  brightness,  and  no  new  star  has  been  found  to 
have  a  measurable  parallax.  Probably  Nova  Andromedae 
was  connected  with  the  nebula  in  which  it  appeared.  The 
new  stars  of  1866  and  1892,  after  droppin^  to  aow  tele- 


UNIVERSITY 


44^  Stars  and  Cosmogony 

scopic  magnitude,  had  a  secondary  rise  in  brightness, 
though  not  to  their  original  magnitude,  after  which  they 
faded  to  their  present  condition  as  very  faint  telescopic 
objects.  Nova  Aurigae  has  become  a  faint  nebulous 
star.  Thorough  search  by  Mrs.  Fleming  of  the  photo- 
graphic charts  and  spectrum  plates  of  the  Harvard  College 
Observatory,  obtained  in  both  hemispheres,  has  led  to  the 
detection  of  many  new  stars  that  would  otherwise  have 
escaped  observation.  Recent  ones  are  Nova  Normae 
(1893),  Nova  Carinae  (1895),  and  Nova  Centauri  (1895). 
Following  are  spectra  of  temporary  stars,  showing  hydro- 
gen and  calcium  lines. 


Spectra  of  New  Stars  (Pickering) 

Spectra  of  New  Stars.  —  The  spectroscope  has  proved  itself  a  power- 
ful adjunct  in  the  observation  of  temporary  stars.  First  employed  on 
the  Nova  of  1866,  it  demonstrated  the  presence  of  incandescent  hydro- 
gen. Nova  Cygni,  ten  years  later,  gave  a  similar  spectrum,  added  to 
which  were  the  lines  of  helium,  long  known  in  the  sun,  but  only  in  1895 
identified  as  a  terrestrial  element.  Nova  Andromedae  (1885)10  most 
observers  presented  a  continuous  spectrum;  but  Nova  Aurigae  (1892) 
gave  a  distinctly  double  and  singularly  complex  spectrum.  Many  pairs 
of  lines  indicated  clearly  a  community  of  origin  as  to  substance,  and 
accurate  measurement  showed  a  large  displacement  which  indicated  a 
relative  velocity  of  nearly  900  kilometers,  or  more  than  500  miles  per 
second;  and  this  type  of  spectrum  remained  characteristic  for  more 
than  a  month.  For  each  bright  hydrogen  line  displaced  toward  the 
red  there  was  a  dark  companion  line  or  band,  about  equally  displaced 
toward  the  violet.  It  was  as  if  the  strange  light  were  due  to  a  solid 


Variables  of  the  Algol  Type 


449 


globe  moving  swiftly  "away  from  us,  and  plunging  into  an  irregular 
nebulous  mass  swiftly  approaching  us.  Tests  for  parallax  placed  Nova 
Aurigae  at  the  distance  of  the  Galaxy,  so  that  this  marvelous  celestial 
display  must  actually  have  occurred  in  space  as  remotely  as  the  begin- 
ning of  the  1 9th  century.  Nova  Normae  was  characterized  by  a  spectrum 
almost  identical  with  that  of  Nova  Aurigae,  as  shown  in  the  photographs 
opposite,  taken  in  Cambridge  and  Peru. 

Irregular  Variables.  —  These  objects  are  not  numerous,  but  some  of 
them  are  very  remarkable ;  for  example,  Eta  Argus,  an  erratic  variable 
in  the  southern  hemisphere  (shown  in  the  midst  of  the  nebulosity  on 
page  428).  Halley,  who  visited  Saint  Helena  in  1677,  recorded  its  mag- 
nitude as  the  fourth.  Between  1822  and  1836  it  fluctuated  between  the 
first  and  second  magnitudes;  but  in  1838  the  light  became  tripled, 
rivaling  all  the  stars  except  Sirius  and  Canopus.  In  1843  it  was  even 
brighter,  but  since  then  it  has  declined  more  or  less  steadily,  reach- 
ing a  minimum  of  the  j\  magnitude  in  1886.  Probably  it  has  no 
regular  period,  although  one  of  a  half  century  has  been  suggested. 
Recently  the  brightness  of  Eta  Argus  has  shown  a  slight  increase. 
A  few  other  stars  vary  in  this  irregular  manner,  though  their  fluctuations 
are  confined  to  a  much  narrower  range. 

Variables  of  the  Algol  Type. —  Algol  is  the  name  of 
the  star  Beta  Persei,  the  best  known  object  of  this  class. 
As  a  rule,  the  periods  of  this 
type  of  variables  are  short, 
and  they  remain  at  maximum 
brightness  during  nearly  the 
whole.  Then  almost  suddenly 
they  drop  within  a  few  hours 
to  minimum  light,  remain  there 
but  a  fraction  of  an  hour,  and 
almost  as  rapidly  return  to  full 
brightness  again.  The  spectra 
of  all  Algol  variables  are  of 
the  first  type. 


Light -Curves  near  Minimum  of  Four 
Algol  Variables  (Pickering) 


The  diagram  represents  the   light-curves  (between  maximum  and 

minimum)  of  four  stars  of  this  type,  as  determined  by  E.  C.  Pickering 

at  the  Harvard  College  Observatory.     The  star  W  Delphini,  although 

telescopic,  is  the  most  pronounced  object  of  this  type  so  far  discovered. 

TODD'S  ASTRON.  —  29 


45°  Stars  and  Cosmogony 

It  remains  at  full  brightness  rather  more  than  four  days  ;  then  from  the 
9.3  magnitude  (upper  left-hand  corner  of  the  diagram)  it  drops  in 
seven  hours  to  the  12.0  magnitude,  becoming  so  faint  as  to  be  invisible 
in  a  four-inch  telescope.  Algol,  in  4^  hours,  drops  a  little  more  than  i  .o 
magnitude,  and  returns  to  its  full  brightness  in  5}  hours,  as  the  curve 
shows.  Its  period,  or  interval  from  one  minimum  to  the  next,  is  very 
accurately  known;  at  present  it  is  2  d.  20  h.  48  m.  55.4  s.,  and  is  very 
gradually  lessening.  At" full  brightness  Algol  is  of  the  2.2  magnitude, 
and  is  therefore  a  conspicuous  star.  It  remains  at  minimum  only  about 
15  minutes.  Algol,  is  best  observed  from  early  autumn  to  the  middle  of 
spring.  Belonging 'to  a  type  regarded  by  some  as  new,  though  at  first 
classified  with  Algol  stars,  are  a  few  such  rapid  variables  as  S  Antliae 
which  was  discovered  by  Paul  in  1888.  These  compound  stars  would 
seem  to  constitute  a  binary  system  whose  members  swing  round  each 
other  almost  in  contact  (page  469). 

Causes  of  Variability.  —  No  general  explanation  seems 
possible  covering  the  variety  in  mutations  of  brightness  of 
all  classes  of  variables.  Those  of  the 
Algol  type  'are  readily  accounted  for  by 
the  theory  of  a  dark  eclipsing  body, 
smaller  than  the  primary,  and  traveling 
round  it  in  an  orbit  lying  nearly  edgewise 
to  us.  The  illustration  shows  this :  in 
the  upper  figure  the  system  appears  as 
we  look  at  it ;  in  the  lower,  as  it  would 
Orbit  of  Algol's  Dark  Seem  if  wecould  look  perpendicularly  upon 

Companion 

it.  Gravitation  of  a  massive  dark  com- 
panion would,  by  its  movement  round  Algol,  displace  it 
alternately  toward  and  from  the  earth,  when  in  the  posi- 
tions E  and  F\  because  the  two  bodies  must  revolve  round 
their  common  center  of  gravity.  Just  such  a  motion  of 
Algol  in  the  line  of  sight  has  been  detected  with  the 
spectroscope,  proving  that  the  star  alternately  recedes 
from  and  advances  toward  us  at  the  rate  of  26  miles  per 
second,  in  a  period  synchronous  with  that  of  its  variability. 

For  variables  of  other  types,  a  comprehensive  explanation  is  found  in 
vast  areas  of  spots,  similar  to  spots  on  the  sun,  taken  in  connection  with 


Double  Stars 

the  star's  rotation  on  its  axis  and  a  periodicity  of  the  spots  themselves. 
The  new  stars  are  more  likely  due  to  tremendous  outbursts  of  glowing 
hydrogen  ;  perhaps  in  some  cases  to  vaporization  of  dark  bodies  caused 
by  their  brushing  past  each  other,  or  to  a  faint  stars  actual  plunging 
through  a  gaseous  region  of  space.  Sir  Norman  Lockyer's  theory  for 
variables  of  the  Omicron  Ceti 
class  is  made  clear  by  the 
illustration  :  variable  stars  are 
still  in  the  condition  of  me- 
teoric swarms ;  and  the  or- 
bital revolution  of  lesser 
swarms  around  larger  aggre- 
gations must  produce  multi- 
tudes of  collisions,  periodically 
raising  hosts  of  meteoric 
particles  to  a  state  of  incan- 
descence. 

Double  Stars. — Many 
stars  which  to  the  unas- 
sisted eye  look  simply  as      Sir  Norman  ^^S^  The°ry  °f 
one,  are  separated  by  the 

telescope  into  more  than  one.  According  to  the  number, 
these  are  called  double,  triple,  quadruple,  or  multiple  stars. 
When  the  components  of  a  pair  appear  to  be  associated 
together  in  space,  it  is  catalogued  as  a  double  star.  A  few 
stars,  however,  are  only  apparently  double,  having  no  actual 
relation  to  one  another  in  space,  and  only  seeming  in 
proximity  because  they  happen  to  be  nearly  in  the  line  of 
sight  from  the  earth.  They  are  remote  from  each  other, 
as  well  as  from  the  solar  system.  Such  pairs  of  stars  are 
called  optical  doubles. 

Although  a  few  double  stars  were  known  earlier,  history  of  the  dis- 
covery and  measurement  of  these  objects  may  be  said  to  have  begun 
with  Sir  William  Herschel  in  1779.  The  Struves,  father  and  son,  and 
Baron  Dembowski,  among  others,  have  prosecuted  these  researches 
vigorously.  More  than  10,000  double  stars  are  now  known,  and  discov- 
eries have  been  rapidly  made  in  recent  years,  particularly  by  Burnham 
of  Chicago.  The  next  illustration  shows  a  dozen  of  the  easier  doubles, 


452  Stars  and  Cosmogony 

within  reach  of  small  telescopes.  Instruments  of  greater  diameter 
than  six  inches  are  necessary  to  divide  the  components  of  a  double 
star  whose  apparent  distance  from  one  another  is  less  than  o".8.  Bond 
and  Gould  were  pioneers  in  the  application  of  photography  to  observa- 
tion of  the  wider  <  doubles  ' ;  but  here  the  assistance  of  this  new  method 
is  not  as  important  as  in  other  departments  of  astronomy.  Among 
other  European  observers  of  double  stars  are  Bigourdan  of  Paris  and 
Glasenapp  of  Saint  Petersburg;  and  in  America  A.  Hall,  Comstock, 
and  Leavenworth. 

Binary  Stars.  —  Careful  and  protracted  observations  are 
necessary  to  determine  the  class  to  which  any  pair  of 
stars  belongs.  If  the  components  of  a  '  double '  are 


Twelve  Typical  Double  Stars 

found  to  revolve  in  a  closed  or  elliptic  orbit,  they  are 
called  a  binary  star.  It  is  assumed,  and  doubtless  rightly, 
that  this  motion  depends  upon  gravitation. 

About  200  binaries  are  now  known,  and  the  orbits  of  perhaps  50  of 
them  are  well  ascertained.  In  his  Researches  on  the  Evolution  of  the 
Stellar  Systems  (1896),  See  has  presented  a  summary  of  present  knowl- 
edge of  these  bodies.  According  to  Miss  Everett's  investigation,  the 
planes  of  their  orbits  sustain  no  definite  relation  to  any  fundamental 


Masses  of  Binary  Stars 


453 


1SO° 


plane  of  the  heavens.  The  star  known  as  ft  883  (star  No.  883  dis- 
covered by  Burnham)  is  the  shortest  known  binary,  its  period  being 
5_V  years  ;  the  longest  is  Zeta  Aquarii,  not  less  than  1500  years.  Several 
binary  stars  are  recognized,  one  component  of  which  is  dark.  These 
can  be  discovered  only  by  the  effect  which  the  attraction  of  the  dark 
star  produces  in  changing  the  position  of  the  bright  one.  The  giant 
Sirius  is  a  star  of  this  kind,  having  a  faint  attendant  only  bright  enough 
to  be  detected  with  large  telescopes,  and  known  as  the  companion  of 
Sirius.  Its  orbit  as  determined  by  Burnham  from  observations  1862-96 
is  shown  adjacent.  Before  actual  discovery  (by  A.  G.  Clark  in  1862), 
not  only  its  existence  but  its  true  position  had  been  predicted  by  Auwers. 
The  companion's  period  is  52 
years ;  and  its  motion,  and 
distance  both  from  Sirius  and 
from  the  solar  system,  show 
that  the  mass  of  the  com- 
panion equals  that  of  the  sun, 
while  that  of  the  Dog  Star  it- 
self exceeds  that  of  the  sun 
2 1  times. 


But  the  best  known 
binary  system  is  the 
one  first  discovered  (by 
Richaud  in  1689),  Al- 
pha Centauri,  also  the 
nearest  of  all  the  fixed  stars, 
first  and  second  magnitude. 


Orbit  of  Sirius  (Burnham) 


Its  components  are  of  the 
The  period  of  the  stars' 
revolution  is  81  years,  the  masses  of  the  two  components 
are  very  nearly  equal,  and  their  combined  mass  is  twice 
that  of  the  sun.  The  stars  of  a  binary  system  are  said  to 
be  in  periastron  when  nearest  to  one  another  in  space ; 
and  in  apastron  when  farthest.  At  periastron  the  com- 
ponents of  Alpha  Centauri  are  about  as  far  apart  as  Saturn 
is  from  the  sun ;  in  apastron  their  distance  from  each 
other  greatly  exceeds  that  of  Neptune  from  us. 

Eccentricities  and  Masses  of  Binary  Stars.  —  The  orbits 
of  binary  stars  are  remarkable  for  great  eccentricity ;  also 
for  the  large  mass-ratios  of  their  components,  always 


454  Stars  and  Cosmogony 

comparable,  and  in  some  cases  nearly  equal.  In  these 
respects  they  differ  greatly  from  the  bodies  of  the  planet- 
ary system,  the  orbits  in  which  are  nearly  circular,  and 
none  of  the  planets  have  more  than  a  small  fraction  of 
the  sun's  mass.  See  explains  the  exceptionally  high 
eccentricity  of  binary  orbits,  according  to  the  principles 
of  tidal  evolution,  from  orbits  which  were  nearly  circular 
in  the  beginning.  Originally  the  system  was  a  single 
rotating  nebulous  mass,  which  became  modified  into  a 
dumb-bell  figure  as  a  result  of  its  own  contraction.  The 
average  eccentricity  of  the  best  known  binaries  is  0.48, 
while  that  of  the  planets  and  satellites  in  our  system  is 
less  than  0.04,  or  only  -^  as  great ;  and  this  extraordinary 
relation  may  be  accepted  as  the  expression  of  a  funda- 
mental law  of  nature.  Recalling  the  principles  by  which 
the  mass  of  a  planet  is  compared  with  that  of  the  sun,  it 
is  evident  that  a  like  method  will  give  the  mass  of  a  binary 
system,  also  in  terms  of  the  sun.  First  we  must  measure 
the  major  axis  of  the  orbit,  and  observe  the  period  of  revo- 
lution ;  also  it  is  necessary  to  assume  that  the  Newtonian 
law  of  gravitation  governs  their  motion.  Then  :  — 

[Moon's  distance!3  ["Distance  between  components!3 

from  earth      J  of  Alpha  Centauri  J 


f  Moon's  sidereal  "I2     f  Earth's  mass! 


x 


r  I2     f  Sum  of  masses  I 
LofcomponentsJ 


L         period         J       L   -f  moon's  J       L    revolution    J       Lof  components. 

Masses  of  the  few  binary  systems  ascertained  in  this  man- 
ner are  about  twofold  or  threefold  that  of  the  sun. 

Binaries  discovered  by  the  Spectroscope.  —  It  was  Bessel 
who  first  wrote  of  the  'astronomy  of  the  invisible,'  and 
his  prediction  has  been  marvelously  fulfilled  by  the  recent 
discovery  of  spectroscopic  binaries.  They  are  binaries 
whose  components  are  so  near  each  other  that  the  tele- 
scope cannot  divide  them,  and  whose  spectra  therefore 
overlie.  As  the  orbits  of  binary  systems  stand  at  all  pos- 


Multiple  Stars 


455 


sible  angles  in  space,  a  few  will  appear  almost  edge  on. 
Let  the  two  components  be  in  conjunction,  as  referred  to 
the  solar  system ;  clearly  their  spectra  will  be  identical. 
But  when  they  reach  quadrature,  one  will  be  receding 
from  the  earth  and  the  other  coming  toward  it.  A  given 
line  in  the  compound  spectrum,  then,  will  appear  double, 
on  account  of  displacement  due  to  motion  of  the  compo- 
nents in  opposite  directions.  Measure  the  displacement,- 
and  observe  the  period  of  its  recurrence.  This  gives  the 
velocity  of  the  components  relatively  to  each  other,  the 
dimensions  of  their  orbit,  and  their  mass  in  terms  of  the 
sun,  always  assuming  that  the  same  law  of  gravitation  is 
regnant  among  the  stars. 

The  binaries  so  far  discovered  by  this  method  have  relatively  short 
periods ;  the  shortest  known  is  /x1  Scorpii,  only  35  hours.  Beta  Aurigae 
is  a  remarkable  star  of  this 
class,  the  doubling  of  its 
lines  taking  place  on  alter- 
nate nights,  giving  a  period 
of  four  days  ;  and  the  com- 
bined mass  of  both  stars 
is  more  than  twice  that 
of  the  sun.  The  region  of 
its  spectrum  is  here  shown, 
with  lines  both  double  and 
single.  New  stars  of  this 
type  are  continually  com- 
ing to  light ;  but  if  the  or- 
bits lie  perpendicular  to  the 
line  of  sight,  the  duplicity  is  not  discoverable  in  this  manner.  The  one 
first  found  by  E.  C.  Pickering  in  1889  is  perhaps  the  most  remarkable 
of  all ;  it  is  Zeta  Ursae  Majoris  (Mizar),  the  K  line  in  whose  spectrum 
becomes  periodically  double,  indicating  a  period  of  about  52  days.  The 
measured  distance  of  the  double  lines  gives  a  relative  velocity  of  100 
miles  per  second,  and  the  mass  of  the  system  exceeds  that  of  the  sun 
forty  fold.  Be'lopolsky's  recent  investigations  with  the  great  Pulkowa 
refractor,  prove  that  a1  Geminorum,  one  of  the  component  stars  of  Cas- 
tor, also  is  a  swift  moving  spectroscopic  binary. 

Multiple  Stars.  —  Numerous  stars  have  more  than  two 


1889,  Dec.  30  d.  17.6  h.,  G.M.T.  (single) 


$89,  Dec.  31  d.  11.5  h.,  G.M.T.  (double) 
Spectra  of  0  Aurigae  (Pickering) 


45 6  Stars  and  Cosmogony 

components  in  the  same  field  of  view.  These  are  gener- 
ally called  multiple  stars,  though  the  terms  triple  star  for 
three  components,  quadruple  for  four,  and  so  on,  are  often 
used.  In  isolated  instances  a  star  may  be  optically  mul- 
tiple; that  is,  the  components  appear  to  be  associated 
together,  from  the  fact  that  they  are  in  or  near  the  line  of 
sight,  while  in  reality  they  are  at  vastly  different  distances 
from  the  sun,  and  are  in  no  sense  related  to  each  other. 
Nearly  all  multiple  stars  are  physically  multiple ;  that  is, 
connected  together  in  a  real  system.  Such  a  system  is  the 
star  Epsilon  Lyrae,  the  well-known  fourth-magnitude  star, 
near  Vega.  A  keen  eye,  even  without  optical  assistance, 
will  split  it  into  a  double.  A  small  telescope  will  divide 
each  of  the  two  components  into  a  pair,  forming  a  beau- 
tiful quadruple  system ;  while  large  telescopes  show  at 
least  three  other  faint  stars,  one  of  them  very  difficult, 
between  the  pairs.  Not  only  do  the  two  stars  of  each  pair 
revolve  round  each  other,  in  periods  of  several  hundred 
years,  but  the  pairs  themselves  have  a  grander  orbital  mo- 
tion round  each  other  in  a  vast  period  not  yet  determined. 
A  multiple  star  having  more  than  seven  or  eight  compo- 
nents would  be  classed  as  a  star  cluster. 

Stellar  Clusters.  —  Seeming  aggregations  of  stars  in  the 
sky  are  called  stellar  clusters,  or  simply  clusters.  Broadly 
speaking,  they  are  embraced  in  two  classes :  The  loose 
clusters,  so  called  because  the  stars  are  not  very  thickly 
scattered,  of  which  the  Pleiades  are  a  very  conspicuous 
type ;  and  the  close  clusters,  in  which  the  stars  appear  to 
be  thickly  aggregated.  The  Pleiades  contain  six  stars  vis- 
ible to  the  ordinary  naked  eye,  though  seven,  nine,  and  even 
as  many  as  thirteen  stars  have  in  rare  instances  been  seen 
in  this  group  without  a  telescope.  A  medium  glass  shows 
about  100  stars,  and  a  photographic  plate  exposed  an 
hour  displays  more  than'  2OOO  stars  in  and  close  to  the 


Stellar  Clusters 


457 


Pleiades.  An  exposure  of  six  hours  shows  4000  stars. 
The  longer  the  exposure,  the  more  stars  appear  on  the 
plate.  By  an  exposure  of  17  h.  30  m.,  continued  on  nine 
nights,  and  covering  a  region  of  four  square  degrees, 
nearly  7000  stars  are  counted  in  the  Pleiades.  Recent 
counts  make  them  fewer  in  the  immediate  regions  of  the 
bright  stars  than  in  adjacent  portions  of  the  sky  of  equal 
area ;  and  very  much  fewer  than  in  many  parts  of  the 
Milky  Way.  Also  by  photography  Barnard  has  discov- 
ered extensive  nebulosities  surrounding  the  Pleiades,  which 
the  glare  of  the  larger  stars  makes  difficult  to  see  with  a 
telescope.  They  have  crudely  the  shape  of  a  horseshoe. 

One  type  of  close  clusters  is  known  as  the  globular  cluster,  in  which 
the  stars  are  compacted  together  as  if  in  a  seemingly  circular  area, 
or  in  space  a  nearly  globular 
mass.  The  adjacent  picture 
is  an  excellent  illustration  of 
this  type.  The  more  nearly 
spherical  a  cluster  is,  the  older 
it  is  thought  to  be ;  for  the  in- 
dividual components  of  clus- 
ters are  no  doubt  subject  to  the 
laws  of  central  attraction,  and 
the  more  perfect  approach  to 
a  spherical  figure  would  indi- 
cate that  the  action  of  central 
forces  had  been  longer  con- 
tinued. Thus  it  is  possible 
to  infer  the  maturity  of  a 
cluster  from  the  relative  dis- 
position of  its  component 
numbers.  One  of  the  finest 
objects  in  the  sky  is  the  double  cluster,  excellently  reproduced  in  the 
next  photograph.  It  forms  part  of  the  Milky  Way  in  Perseus,  and  each 
component  approaches  the  globular  form.  The  clusters  are  made  up  of 
stars  of  all  sizes,  and  are  without  doubt  at  stellar  distances  from  us, 
though  no  parallax  of  a  cluster  has  yet  been  measured.  In  all,  about 
200  clusters  and  nebulae  have  been  photographed,  so  that  a  half  century 
hence  it  may  be  possible  to  ascertain  what  changes  are  taking  place. 


Globular  Cluster  15  Pegasi  (Roberts) 


45^ 


Stars  and  Cosmogony 


The  Galaxy,  or  Milky  Way.  —  Lying  diagonally  across 
the  dome  of  the  sky,  at  varying  angles  and  elevations  in 
different  seasons  of  the  year,  may  be  seen  on  clear,  moon- 
less nights  an  irregular  belt  or  zone  of  hazy  light  of  uneven 


The  Double  Cluster  in  Perseus  (photographed  by  Roberts) 

brightness,  about  three  times  the  breadth  of  the  moon, 
and  stretching  from  horizon  to  horizon.  This  is  part  of 
the  Galaxy,  or  Milky  Way.  It  is  really  a  ring  of  light, 
reaching  entirely  round  the  celestial  sphere,  roughly  in  a 
great  circle ;  and  usually  about  half  of  it  will  be  above  the 
horizon  and  half  below.  It  intersects  the  ecliptic  near  the 
solstices,  at  an  angle  of  about  60°.  Early  in  September 


Stellar  Distribution  459 

evenings  it  nearly  coincides  with  a  vertical  circle  lying 
northeast  and  southwest.  The  Galaxy  is  fixed  in  relation 
to  the  stars,  and  part  of  it  lies  so  near  the  south  pole  of 
the  heavens  that  it  can  never  be  seen  in  our  northern 
latitudes.  From  Cygnus  to  Scorpio  it  is  a  divided  belt,  or 
double  stream.  Even  a  small  telescope  shows  at  once 
that  the  Milky  Way  is  composed  of  millions  of  faint  stars, 
nearly  every  one  of  them  individually  too  faint  for  naked- 
eye  vision,  but  whose  vast  numbers  give  us  collectively 
the  gauzy  impression  of  the  Galaxy.  On  page  13  is  an 
excellent  reproduction  from  one  of  the  finest  of  Barnard's 
photographs  of  the  Milky  Way,  and  equally  striking  photo- 
graphs have  been  obtained  by  Wolf,  and  of  the  Southern 
Milky  Way  by  Russell.  All  these  stars  are  suns,  and 
probably  comparable  in  size  and  constitution  with  the 
sun  himself. 

They  are  not  evenly  scattered,  but  in  many  regions  are  aggregated 
into  close  clusters  of  stars  ;  for  example,  the  double  cluster  in  the  sword 
hilt  of  Perseus,  shown  opposite.  It  is  readily  visible  to  the  naked  eye 
on  clear,  moonless  nights  in  the  position  shown  in  diagram  on  page  66. 
According  to  Easton,  the  galactic  system  accessible  to  our  observation 
has  but  little  depth  in  proportion  to  its  diameter.  Study  of  the  photo- 
graphs has  led  Maunder  to  direct  attention  to  'dark  lanes '  in  the  Milky 
Way,  marking  regions  of  real  barrenness  of  stellar  material,  and  per- 
haps indicant  of  galactic  condensation  progressing  toward  an  ultimate 
globular  cluster. 

Distribution  of  the  Stars.  —  As  to  their  apparent  dis- 
tribution over  the  face  of  the  sky,  lack  of  uniformity  is 
evident.  The  fact  of  their  recognized  division  into  con- 
stellations, even  from  the  earliest  -ages,  is  proof  of  this. 
Clusters  and  starless  vacuities  are  well  known.  Frequently 
there  are  found  streams  of  stars,  especially  by  exploration 
with  the  telescope.  One  general  law  is  known  to  govern 
the  apparent  distribution  in  the  heavens :  at  both  poles  of 
the  Milky  Way,  the  stars  are  scattered  most  sparsely ; 


460 


Stars  and  Cosmogony 


and  the  number  in  a  unit  of  surface  of  the  stellar  sphere 
increases  on  all  sides  uniformly  toward  the  plane  of  the 
Milky  Way  itself.  This  important  discovery  was  made  by  Sir 
William  Herschel,  through  a  laborious  process  of  actually 
counting  the  stars,  technically  called  '  star  gauges.'  In 
Coma  Berenices,  for  example,  near  the  north  pole  of  the 
Milky  Way,  are  perhaps  five  stars  in  a  given  area  ;  half 
way  to  the  Galaxy  the  number  has  doubled  ;  and  in  the 
Milky  Way  itself  the  average  number  is  found  to  exceed 
1  20,  thus  increasing  more  rapidly  as  this  basal  plane  of 
the  sidereal  universe  is  approached.  Kapteyn,  a  recent 
investigator  of  this  supreme  problem,  likens  the  general 
shape  of  the  stellar  universe  to  that  of  the  great  nebula  in 
Andromeda  (opposite);  the  disk-shaped  nucleus  represent- 
ing the  cluster  to  which  the  sun  belongs,  and  its  exterior 
rings  the  flattened  layers  of  stars  surrounded  by  the  zone 
of  the  Galaxy. 

The  Nebulae.  —  A  nebula  is  a  celestial  object,  often  of 
irregular  form  and  brightness,  appearing  like  a  mass  of 

luminous  fog.  In  all, 
about  8000  are  now 
known,  and  their  posi- 
tions among  the  stars 
determined.  They  differ 
greatly  in  brightness, 
form,  and  apparent  size. 
Many  of  them  are  shown 
by  the  spectroscope  to 
be  glowing,  incandescent 
gases,  in  large  part  hy- 
drogen. These  are  green- 
ish in  tint;  but  a  few 

Ring  Nebula  in  Lyra  (Roberts) 


able;   that  is,  composed  of  masses  of  separate  stars  too 


Remarkable  Nebulce 


461 


faint  to  be  seen  individually.  The  nebulae  appear  like  the 
residue  of  the  materials  of  original  chaos  out  of  which  the 
sun,  his  planets,  and  the  stars  have  through  many  millions 
of  years  come  into  being.  A  few  of  them  are  variable  in 
brightness. 

Classification  of  the  Nebulae.  —  It  is  usual  to  divide  the 
nebulae  into  five  classes,  based  on  their  various  forms: 
(i)  annular  nebulae,  (2)  spiral  nebulae,  (3)  planetary  nebulae, 
(4)  nebulous  stars,  (5)  irregular  nebulae,  for  the  most  part 
large.  A  sixth  class,  elliptic  nebulae,  is  sometimes  recog- 
nized; probably  they  are  annular  nebulae  seen  edgewise,  or 
nearly  so.  But  some  of  the  so-called  annular  nebulae  ap- 
pear elliptic  also.  Every  degree  of  eccentricity  in  their 
figure  is  recognized  —  some  are  merely  oval,  others  are 
drawn  out  (page  469)  into  a  mere  line.  Swift  has  made 
numerous  nebular  discoveries,  and  the  most  extensive  cata- 
logue of  nebulae  is  by  Dreyer. 

By  prolonged  exposures 
fine  photographs  of  the  fainter 
nebulae  have  been  obtained 
by  von  Gothard  and  others. 
A  famous  nebula  of  the  irreg- 
ular order  surrounds  the  star 
Eta  Argus  (page  428).  In 
recent  years  it  has  been  fre- 
quently photographed  by  Gill 
and  Russell  with  exposures  of 
many  hours'  duration,  and 
changes  in  its  brightness  are 
plainly  indicated. 

Remarkable  Annular  and 
Elliptic  Nebulae.  — A  fine  ob- 
ject of  this  class  was  dis- 
covered by  Gale  in  1894  in 
the  southern  constellation 
Grus  ;  but  the  best-known  The  Great  Nebula  in  Andromeda  (Roberts) 

annular  nebula  is  in  the  con- 
stellation Lyra.     A  very  faint  object  in  small  telescopes,  the  great  ones 


462  Stars  and  Cosmogony 

reveal  many  stars  within  its  interior  spaces.  The  illustration  on  p.  460 
is  from  a  photograph  of  the  nebula,  but  it  does  not  show  the  complexity 
and  irregularity  of  structure  which  some  of  the  large  telescopes  indicate. 
The  star  near  its  center  is  thought  to  be  variable.  Among  elliptic  neb- 
ulae, the  signal  object  is  the  'great  nebula  in  Andromeda.'  So  bright  is 
it  that  the  unaided  eye  will  recognize  it,  near  Eta  Andromedae.  Its  vast 
size,  too,  as  seen  in  the  telescope,  is  remarkable  —  about  seven  times 
the  breadth  of  the  moon,  and  its  width  more  than  half  as  great.  The 
illustration  shows  its  striking  structure,  first  clearly  revealed  by  Rob- 
erts's  splendid  photographs  in  1888.  Apparently  it  is  composed  of  a 
number  of  partially  distinct  rings,  with  knots  of  condensing  nebulosity, 
as  if  companion  stars  in  the  making.  Its  spectrum  shows  that  it  is  not 
gaseous,  still  no  telescope  has  yet  proved  competent  to  resolve  it. 

Spiral  and  Planetary  Nebulae.  —  The  great  reflecting  tel- 
escope of  Lord  Rosse  first  brought  to  light  the  wonderful 

spiral  nebulae,  the  most 
conspicuous  example  of 
which  is  found  in  Canes 
Venatici.  Its  structure 
is  such  that  photography 
has  a  vast  advantage  in 
depicting  it,  as  the  ad- 
jacent illustration  re- 
veals. The  convolutions 
of  the  spiral  are  filled 
with  many  star-like  con- 
densations, themselves 
surrounded  by  nebulos- 

Spiral  Nebula  in  Canes  Venatici  (Roberts)          '..  T-,, 

ity.     The   spectroscope 

indicates  its  stellar  character,  though,  like  the  Andromeda 
nebula,  it  is  yet  unresolved,  except  in  parts.  Planetary 
nebulae  have  this  name  because  they  exhibit  a  disk  with 
pretty  definite  outlines,  round  or  nearly  so,  like  the  large 
planets,  though  very  much  fainter.  They  are  nearly  all 
gaseous  in  composition.  Nebulous  stars  are  stars  com- 
pletely enveloped  as  if  in  hazy,  nebulous  fog.  They  are 


Great  Nebula  in  Orion 


463 


mostly  telescopic  objects,  and  very  regular  in  form,  some 
with  nebulosity  well  denned,  others  less  so.  One  has 
luminous  rings  surrounding  it. 

Spectra  of  the  Nebulae.  —  Sir  William  Huggins,  who  in  1864  first 
applied  the  spectroscope  to  nebulae,  discovered  bright  lines  in  their 
spectra,  indicating  a  community  of  chemical  composition,  due  to 
glowing  gas,  in  large  part  hydrogen.  Helium  has  recently  been 
added ;  but  other  lines  are  due  to  substances  not  yet  recognized  as  ter- 
restrial elements.  The  annular,  planetary,  and  mostly  the  irregular  neb- 
ulae give  the  gaseous  spectrum  ;  and  exceedingly  high  temperatures  are 
indicated,  or  else  a  state  of  strong  electric  excitement.  Both  tempera- 
ture and  pressure  appear  to  increase  toward  the  nucleus  of  the  nebula. 
Many  nebulae  fail  to  yield  bright  lines ;  showing  rather  a  continuous 
spectrum,  prominently  the  great  nebula  of  Andromeda.  Lack  of  lines 
may  be  interpreted  as  due  to  gases  under  extreme  pressure,  or  to  ag- 
gregations of  stellar  bodies.  Another  object  of  this  character  is  the 
great  spiral  nebula  in  Canes  Venatici,  well  depicted  in  the  photograph 
by  Roberts  (opposite)  ;  but  no  telescope  has  yet  been  able  to  resolve 
either  of  these  objects  into  discrete  stars.  The  application  of  photog- 
raphy has  revealed  about  40  lines  in  the  spectra  of  nebulae  ;  and  Keeler 
and  Campbell  have  shown,  in  the  case  of  the  Orion  nebula,  that  nearly 
every  line  in  its  spectrum  is  the  counterpart  of  a  prominent  dark  line  in 
the  spectra  of  the  brighter  stars  of  the  same  constellation. 

The  Great  Nebula  in 
Orion.  —  Just  below  the 
eastern  end  of  Orion's 
belt  is  this  greatest  of  all 
nebulae.  So  characteris- 
tically bright  is  this  well- 
known  object  that  it  is 
readily  distinguished 
without  a  telescope.  It 
was  the  first  nebula 
ever  photographed  —  by 
Henry  Draper  in  1880. 
The  spreading  expanse 
of  its  nebulosity  completely  envelopes  the  multiple  star 


The  Great  Nebula  in  Orion  (Roberts) 


464  Stars  and  Cosmogony 

Theta  Orionis,  often  called  the  'trapezium'  (not  well  shown 
in  the  photograph  because  the  blur  of  the  nebula  overlaps 
it).  In  small  instruments  a  very  obvious  feature  is  the 
wide  opening  at  one  side,  or  break  in  the  general  light, 
sometimes  called  the  '  Fish's  mouth.'  A  curdling  or  floc- 
culent  structure  is  excellently  shown  in  the  best  photo- 
graphs, and  a  greenish  tinge  has  been  recognized  in  its 
light.  Extensive  wisps  of  nebulosity  reach  out  in  many 
directions,  involving  other  stars.  W.  H.  Pickering's  plates 
indicate  an  approach  to  the  spiral  figure  in  these  outlying 
filaments,  and  Roberts's  photographs  show  vortical  areas 
within  the  nebula.  Its  spectrum  reveals  incandescent 
hydrogen  and  helium;  also  other  substances  not  yet  recog- 
nized among  terrestrial  elements.  The  nebula  is  as  remote 


Path  of  Milky  Way  and  Distribution  of  Nebulae  (according  to  Proctor) 

as  the  stars  are ;  and,  according  to  Keeler's  observations, 
its  distance  from  the  sun  is  increasing  at  the  rate  of  1 1 
miles  every  second.  Also  they  prove  an  intimacy  of  rela- 
tion between  the  nebula  and  neighboring  stars.  There  is 
no  conclusive  evidence  of  change  of  form  in  any  part  of 
the  nebula,  although  H  olden  has  investigated  this  question 


The  Cosmogony  465 

fully.  He  found,  however,  fluctuations  of  brightness  in 
several  regions,  which  Stone  is  now  studying  critically. 

Distribution  of  the  Nebulae.  —  It  may  be  said  that  the 
nebulae  are  distributed  over  the  sky  in  just  the  opposite 
manner  from  the  stars ;  for  their  number  has  a  definite 
relation  to  the  Milky  Way.  Reference  to  the  preceding 
figure  will  show  this  at  a  glance.  The  small  dots  rep- 
resent nebulae,  not  stars ;  and  it  is  at  once  evident  that 
they  are  more  strongly  clustered  the  greater  their  angular 
distance  from  the  Milky  Way.  The  physical  reason  under- 
lying this  fact  is  not  known.  Neither  is  the  distance  of 
any  nebula  known.  So  that  the  distribution  of  the  nebulae 
throughout  space  can  only  be  surmised.  Measurement 
of  the  distance  of  a  few  nebulae  has  been  attempted,  with 
the  disappointing  outcome  that  their  parallax  is  exceedingly 
small,  and  probably  beyond  our  power  ever  to  ascertain. 
They  are,  therefore,  at  distances  from  our  solar  system 
estimable  in  light  years,  like  those  of  the  stars.  Keeler's 
spectroscopic  observations  prove  that  the  nebulae  are  mov- 
ing in  space  at  velocities  comparable  with  those  of  the 
stars;  the  bright  nebula  in  Draco,  for  example,  is  coming 
toward  the  earth  at  the  rate  of  40  miles  every  second. 
None  of  the  nebulae,  however,  have  yet  been  discovered  to 
partake  of  proper  motion. 

The  Cosmogony.  —  Cosmogony  is  the  science  of  the 
development  of  the  material  universe.  It  has  nothing  to 
do  with  the  origins  of  matter,  and  is  concerned  only  with 
its  laws  and  properties,  and  the  transformations  resulting 
from  them.  The  ancient  philosophers  avoided  the  ques- 
tion of  the  origin  of  matter  by  asserting  that  the  universe 
always  had  its  present  form  from  eternity ;  many  minds 
are  still  satisfied  with  a  literal  interpretation  of  the  Old 
Testament  account  of  the  creation,  that  the  Almighty 
Power,  out  of  nothing,  built  the  universe  in  six  days,  sub- 
TODD'S  ASTRON.  —  30 


466  Stars  and  Cosmogony 

stantially  as  observed  in  our  own  age ;  according  to  the 
accepted  cosmogony,  the  universe  was  in  the  beginning 
a  widely  diffused  chaos,  'without  form  and  void/  accord- 
ing to  the  Scriptures.  Out  of  it  has  been  evolved,  by  the 
long-continued  action  of  fixed  natural  laws,  the  present 
orderly  system  of  the  universe. 

The  Universe  is  exceedingly  Old.  —  In  outline,  the  ac- 
cepted cosmogony  is  this :  Once  in  the  inconceivably 
remote  past,  many  hundreds  of  millions  of  years  ago, 
all  the  matter  now  composing  earth,  sun,  planets,  and 
stars,  was  scattered  very  thinly  through  the  untold  vast- 
ness  of  the  celestial  spaces.  The  universe  did  not  then 
exist,  except  potentially.  Then,  as  now,  every  particle  of 
matter  attracted  every  other  particle,  according  to  the 
Newtonian  law.  Gradually  centers  of  attraction  formed, 
and  these  centers  pulled  in  toward  themselves  other  par- 
ticles. As  a  result  of  the  inward  falling  of  matter  toward 
these  centers,  the  collision  of  its  particles,  and  their  fric- 
tion upon  each  other,  the  material  masses  grew  hotter  and 
hotter.  Nebulae  seeming  to  fill  the  entire  heavens  were 

formed  —  luminous  fire 
mist,  like  the  filmy  ob- 
jects still  seen  in  the 
sky,  though  vaster,  and 
exceedingly  numerous. 

Stars   and   Suns  from 
Nebulous    Fire    Mist.  - 
Countless  ages  elapsed; 
the    process     went     on, 

Ideal  Genesis  of  Planetary  System  Swifter    in    SOme    regions 

(Compare  with  actual  nebula  on  page  461)  Qf    space    than   jn    Qthers> 

Millions  upon  millions  of  nebular  nuclei  began  to  form; 
condensation  progressed ;  because  the  particles  could  not 
fall  directly  toward  their  centers  of  attraction,  vast  nebular 


Nebular  Hypothesis  467 

whirlpools  were  set  in  motion  ;  axial  rotation  began  ;  and 
temperature  rose  inconceivably  high  at  centers  where 
condensation  was  greatest.  The  sun  was  one  of  these 
centers ;  earth  and  all  the  other  planets  had  not  yet  a 
separate  existence,  but  the  materials  now  composing  them 
were  diffused  through  the  great  solar  nebula.  Every  star, 
whether  lucid  or  telescopic,  was  such  a  center,  or  be- 
came one  in  the  gradual  evolution  and  process  of  world 
building. 

Planets  from  Nebulous  Stars.  —  As  contraction  and  con- 
densation went  on,  the  whirling  became  swifter,  because 
gravitation  brought  the  particles  nearer  to  the  axis  round 
which  they  turned,  and  there  was  no  loss  of  rotational 
moment  of  momentum.  Centrifugal  force  gave  the  whole 
rotating  mass  the  figure,  first  of  an  orange,  then  of  a  vast 
thickened  disk,  shaped  like  a  watch.  Eventually  the 
masses  composing  its  rim  could  no  longer  whirl  round 
as  swiftly  as  the  more  compact  central  mass ;  so  a  sepa- 
ration took  place,  the  outlying  nebulous  regions  being  left 
or  sloughed  off  as  a  ring,  while  all  the  central  portion  kept 
on  shrinking  inward  from  it.  As  shown  opposite,  the  mass 
of  the  ring  would  rarely  be  distributed  uniformly  ;  but  being 
lumpy,  the  more  massive  portions  would  in  time  draw  in 
the  less  massive  ones,  and  the  ring  would  thus  become  a 
planet  in  embryo ;  and  its  time  of  revolution  round  the 
sun  would  be  that  of  the  parent  ring.  If  still  nebulous, 
the  planet  would  itself  go  through  the  stages  of  the  solar 
nebula,  and  slough  off  rings  to  gather  into  moons  or 
satellites.  Meanwhile  the  parent  nebula  went  on  'con- 
tracting, and  leaving  other  rings,  which  in  the  lapse  of 
ages  developed  into  inner  planets,  and  their  rings  as  a  rule 
into  satellites. 

Early  History  of  the  Nebular  Hypothesis.  —  Such  in  bare 
outline  is  the  nebular  hypothesis.  Note  that  it  is  merely  a 


468  Stars  and  Cosmogony 

highly  plausible  theory ;  it  has  never  been  absolutely  demon- 
strated, and  probably  never  can  be.  To  its  development 
many  great  minds  have  contributed.  The  Englishman 
Thomas  Wright,  the  Swede  Emanuel  Swedenborg,  and  the 
German  Immanuel  Kant,  all,  independently  and  during 
the  1 8th  century,  appear  to  have  originated  the  hypothe- 
sis under  slightly  variant  forms.  Of  these,  Kant's  theory 
was  the  most  philosophic;  but  his  greater  renown  as  a 
mental  philosopher  than  as  a  physicist  appears  to  have 
hindered  attention  to  his  important  speculation.  When, 
however,  La  Place  lent  the  weight  of  his  great  name  to 
an  almost  identical  hypothesis,  astronomers  at  once  recog- 
nized that  it  must  be  based  on  sound  dynamic  concep- 
tions. Then  came  the  giant  telescopes  of  the  Herschels, 
father  and  son,  and  of  Lord  Rosse,  adding  the  evidence  of 
observation ;  for  they  discovered  in  the  sky  nebulae,  some 
globular  in  figure,  some  disk-like,  others  annular,  and  still 
others  even  spiral. 

Later  Developments.  —  But  Lord  Rosse's  great  telescope 
showed,  too,  that  some  at  least  of  the  nebulae  might  be  re- 
solved into  stars,  thereby  threatening  the  subversion  of 
the  nebular  hypothesis,  especially  if  all  the  nebulae  could 
be  so  resolved.  Within  a  few  years,  however,  and  just 
after  the  middle  of  the  iQth  century,  application  of  the 
principles  of  spectrum  analysis  to  the  nebulae  proved 
conclusively  that  many  of  them  are  composed  of  glowing 
gas,  and  therefore  cannot  be  resolved  into  stars.  About 
the  same  time  von  Helmholtz  advanced  the  accepted  theory 
of  the  sun's  contraction  in  explanation  of  the  maintenance 
of  solar  heat;  and  Lane,  an  American,  proved  that  a 
gaseous  mass  condensing  as  a  result  of  gravitation  might 
actually  grow  hotter,  in  spite  of  its  immense  losses  of  heat. 
Thus  it  was  unnecessary  to  assume  a  high  temperature  of 
the  nebula  in  the  beginning.  Also  the  genius  of  Lord 


Darwin  and  See 


469 


Kelvin,  the  eminent  English  physicist,  strengthened  the 
hypothesis  by  computations  on  the  heat  of  the  sun,  and 
his  probable  duration  of  about  20,000,000  years  in  the 
past. 

Recent  Additions.  —  Then  came  Darwin,  who,  in  the 
latter  part  of  the  iQth  century,  demonstrated  mathemati- 
cally the  remarkable  effects  producible  by  tidal  friction, 
which  had  been  neglected  in  all  previous  researches.  The 
gathering  of  a  ring  into  an  embryo  planet  was  a  process 
not  easy  to  explain ;  and  Darwin  showed  that  probably 
the  moon  had  never  been  a  ring  round  the  earth,  but  that 
she  separated  from  her  parent  in  a  globular  mass,  in  con- 
sequence of  its  too  rapid  whirling.  He  showed,  too,  how 
the  mutual  action  of  great  tides  in  the  two  plastic  masses 
would  operate  to  push  the  moon  away  to  her  present  re- 
mote distance  :  the  terrestrial  tidal  wave  being  in  advance 
of  the  moon,  our  satellite  would  tend  to  draw  it  backward ; 
also,  the  wave  would  tend  to  pull  the  moon  forward,  thereby 
expanding  her  orbit,  and  increasing  her  mean  distance  from 
us.  His  researches  cleared  up,  also,  the  enigma  of  the 
inner  satellite  of  Mars,  revolving  round  its  primary  in  less 
time  than  Mars  himself  turns  on  his  axis ;  and  no  less  the 
newly  discovered  fact 
that  Mercury  and  Venus 
keep  a  constant  face  to 
the  sun,  and  satellites  of 
Jupiter  to  their  primary, 
just  as  the  moon  to  the 
parent  earth.  Still  later, 
by  adapting  these  prin- 
ciples to  stellar  systems, 

See  explained  the  fact  Of  •    Various  Types  of  Double  Nebulae  (Lord  Rosse) 

the  great  eccentricity  of 

the  binary  orbits  as  a  result  of  the  long-continued  or  secu- 


470  Stars  and  Cosmogony 

lar  action  of  tidal  friction.  The  double  stars,  then,  were 
originally  double  nebulae,  separated  by  a  process  resem- 
bling '  fission '  in  the  case  of  protozoans.  Poincare  has 
proved  mathematically  that  a  whirling  nebula,  in  conse- 
quence of  contraction,  is  liable  to  distortion  into  a  pear- 
shaped  or  hour-glass  figure,  and  to  ultimate  separation. 
And  there  is  excellent  observational  proof  in  the  double 
nebulae  (p.  469)  found  in  different  regions  of  the  heavens. 

Evidence  supporting  the  Nebular  Hypothesis. — To  collect 
evidence  from  the  entire  universe,  as  at  present  known  :  — 

(<?)  Scanning  the  heavens  with  the  telescope,  we  find 
numerous  nebulae  of  forms  required  by  the  theory. 

(£)  Spectrum  analysis  proves  a  general  unity  of  chemical 
composition  throughout  the  universe. 

(c)  Stellar  evolution  necessitates  the  supposition  of  birth, 
growth,  and  decay  of  stars,  —  a  requirement  met  by  the  fact 
that  types  of  stellar  spectra  differ  greatly,  possibly  indica- 
ting a  wide  variation  in  age  of  the  stars,  although  this  is 
not  yet  clearly  made  out  in  all  detail. 

(d)  Our  sun  is  a  star,  and  its  corona  resembles  such 
wisps  of  nebulous  light  as  theory  would-  lead  us  to  expect. 

(e)  The  maintenance  of  solar  heat  is  best  explained  on 
the  basis  of  the  sun's  continual  contraction. 

(/)  The  planets  revolve  round  the  sun,  and  the  satellites 
round  the  planets,  in  nearly  the  same  plane  (with  few  ex- 
ceptions not  difficult  to  account  for). 

(g)  The  planets  all  rotate  on  their  axes  (so  far  as 
known),  also  revolve  in  their  orbits  round  the  sun,  in  the 
same  direction. 

(/z)  The  zone  of  small  planets  circling  about  the  sun, 
and  the  triple  ring  surrounding  the  planet  Saturn,  are 
eminently  suggestive  and  seemingly  permanent  illustra- 
tions of  a  single  stage  of  the  interrupted  process  of  world 
building  in  accordance  with  the  nebular  hypothesis. 


Other  Universes  471 

Other  Universes  than  Ours.  —  When  considering  known 
stellar  distances,  we  found  stars  immensely  remote  from 
the  solar  system  in  all  directions ;  and  everywhere  scat- 
tered among  myriads  remoter  still,  whose  distances  we  can 
see  no  prospect  of  ever  ascertaining.  What  is  beyond  ? 
Outside  the  realm  of  fact,  imagination  alone  can  answer. 
We  cannot  think  of  space  except  as  unlimited.  The  con- 
cept of  infinite  space  precludes  all  possibility  of  a  boun- 
dary. But  the  number  of  stars  visible  with  our  largest 
telescopes  is  far  from  infinite ;  for  we  should  greatly  over- 
estimate their  number  in  allowing  but  ten  stars  to  every 
human  being  alive  this  moment  upon  our  little  planet. 
Are,  then,  the  inconceivable  vastnesses  of  space  tenanted 
with  other  universes  than  the  one  our  telescopes  unfold  ? 
We  are  driven  to  conclude  that  in  all  probability  they  are. 
Just  as  our  planetary  system  is  everywhere  surrounded  by 
a  roomy,  starless  void,  so  doubtless  our  huge  sidereal  clus- 
ter rests  deep  in  an  outer  space  everywhere  enveloping 
inimitably.  So  remote  must  be  these  external  galaxies 
that  unextinguished  light  from  them,  although  it  speeds 
eight  times  round  the  earth  in  a  single  second,  cannot 
reach  us  in  millions  of  years.  Verily,  infinite  space  tran- 
scends apprehension  by  finite  intelligence.  Let  us  end 
with  Newton,  as  we  began.  '  Since  his  day,'  wrote  one 
of  England's  greatest  astronomers  in  his  Cardiff  address 
(1891),  'our  knowledge  of  the  phenomena  of  Nature  has 
wonderfully  increased;  but  man  asks,  perhaps  more 
earnestly  now  than  then,  what  is  the  ultimate  reality 
behind  the  reality  of  the  perceptions  ?  Are  they  only  the 
pebbles  of  the  beach  with  which  we  have  been  playing  ? 
Does  not  the  ocean  of  ultimate  reality  and  truth  lie 
beyond  ? ' 


INDEX 


Abbe,  E.,  Dir.  Obs.  Univ.  Jena  199 
Aberration,    annual    162,    constant    of    163, 

ellipses  164,  437,  stellar  164 
Aberration  time  329 
Achernar  (a  Eridani)  423 
Actinometer  194 

Adams,  J.  C.  (1819-92),  Eng.  ast.  369,  370 
Agathocles  (B.C.  320),  eclipse  of  289 
Alaska  transferred  to  U.  S.  188 
Albategnius,  M.  J.  (A  D.  900),  Arab.  ast.  247 
Aldeb  aran,  Plate  iv.  62,  423,  434,  439,  441 
d'Alembert,  J.  B.  le  R.  (da-long-ber)  (1717- 

83),  Fr.  math.  247 

Alexander,  S.  (1806-83),  Am.  ast.  296 
Algol,  Plate  in.  60,  441,  446,  450 
Almagest  of  Ptolemy  313 
Al-Mamun  (A.D.  810),  Arab,  caliph  80 
Almanac,  Nautical  112,  170 
Almucantar  defined  28 
Alpheratz  (a  Andromedae)  66 
Altair,  Plate  iv.  62,  423,  434,  439,  441,  445 
Altazimuth  48,  81 

Altitude,  defined  47,  58,  measuring  181 
Amherst  College,  lunar  eclipse  at  308,  mete- 
orite collection  412,  418,  419 
Anaximan'der  (B.C.  580),  Gk.  phil.  23,  76 
Andromeda,  Plate  in.  60,  Plate  iv.  62,  nebula 

in  462,  new  star  in  447 
Andromedes,  meteors  403,  414,  417 
Angle  of  the  vertical  87 
Angles,  instruments  for  measuring  193,  208, 

measure  of  44,  relation  to  distance  45 
Anta'res(a  Scorpii),  Plate  iv.  62,  423,  425,442 
Apastron  defined  453 
Aphelion  defined  139 
Apogee,  moon's  233 
Ap'sides,  line  of,  defined  139 
Aquarids,  Delta,  Eta,  meteors  414 
Aquarius,  Plate  iv.  62 
Aquija,  Plate  iv.  62 
Archime'des  (B.C.  250)  Gk.  geom.  247 
Arcturus,  Plate  iv.  62,  423,  439,  441,  444 
Argelander,  F.  W.  A.  (1799-1875),  Ger.  ast. 

424,  425 

Argo,  Plate  iv.  62 
Argus,  Eta,  nebuli  428,  449,  461 
Ariel,  satellite  of  Uranus  347 
Aries,  Plate  iv.  62,  First  of  38,  109 
Aristarchus  (B.C.  270),  Gk.  ast   247 
Aristotle  (B.C.  350)  Gk.  phil    80,  247 
d'Arlandes,    F.    L.   (dar-lond')    (1742-1809), 

Fr.  marquis  291 

Arzachel,  A.  (A  D.  1080),  Heb.  ast.  247 
Assyria,  chronology  of  8,  tablets  289 
Asteroids  314,  335,  361,  362 
Astrographic  charts  427 
Astrolabe,  ecliptic  57 
Astronomer  Royal  433 
Astronomy,  beiore  telescopes  190,  defined  7, 

history  7,  43,  57,  76,  80,  81,  97,  114,  129-31, 

166,  190,  199,  203,  language  of  22,  practical 

defined  43,  utility  of  8 


Atmosphere,  of  earth  90-4,  of  moon  243,  of 

stars  426,  of  sun  279,  steady  191 
Auriga,  Plate  in.  60,  Plate  iv.  62,  447-9 
Aurigse,  Beta  455 
Aurora  94,  spectrum  94 
Autumn  in  general  153,  months  of  159 
Auwers,  A.  (ow'verz),Ger.  ast.  261,430 
Axis,  optical  195 
Azimuth  defined  47,  58 

Bache,  A.  D.  (bach)  (1806-67),  Am.  physicist 

444 

Bailey,  S.  I.,  Am.  ast.  428,  446 
Ball,  Sir  R.  S.,  Dir.  Obs.  Cambridge,  Eng. 

64,  440 
Barnard,  E.  E.,  Prof.  Univ.  Chicago,  4, 13,  18, 

33.  34,  3°7,  335,  344,  352,  357,  393,  401,  405, 

406,  408,  411,  457,  459 
Bede  (bead)  '  The  Venerable '  (A.D.  700),  Eng. 

author  76 
Beer,  W.   (bay'er)   (1797-1850),  Ger.  banker 

and  ast.  355 

Bdopolsky,  A.,  ast.  Pulkowa  Obs.  455 
Berliner  Astron.  Jahrbuch  362 
Bessel,   F.   W.    (1784-1846),   Ger.   ast.    437, 

454 
Betelgeux    (bet-el-gerz')    Plate    iv.   62,   423, 

v.4Bie'la? V  (be'la)  (1782-1856),  Aus.  officer 

401,  403,  411,  418 
Bielids  (be'lidz),  meteors  403,  418 
Bigelow,  F.  H.,  U.  S.  Weather  Bureau  300 
Bigourdan,G.  (be-goor-dong  ),ast.  Paris  Obs. 

.452 
Binary  stars  452,  eccentricities  453,  masses 

453,  spectroscopic  454 

Bisch'ofiTsheim,  R.,  Fr.  banker  and  patron  202 
Blanpain,  M.  (1779-1843),  Fr.  ast.  401 
Bode,  J.  E.   (bo'duh)  (1747-1826),  Ger.  ast., 

law  of  333,  361 
Bolometer  194,  277 

Bond,  G.  P.  (1825-65),  Am.  ast.  368,  452 
Bond,  W.  C.  (1789-1859)  Am.  ast.  346 
Bootes,  Plate  in.  60,  Plate  iv.  62 
Boss,  L.,  Dir.  Dudley  Obs.  427,  431 
Box-transit  118 
Boyden,  U.  A.  (1804-79),  Am.  engineer  and 

patron  192,  444 
Brachy-telescope  204 
Bradley,  J.  (1693-1762),  Ast.  Royal  163 
Brashear,  J.  A.  191,  203,  205,  272,  281 
Bredichin,  T.  (bray-de-kang  ),  Russ.  ast.  396 
Brenner,  L.,  ast.  Obs.  Lussinpicolo  369,  370 
British  Museum  meteorites  412,  419 
Brooks,  W.  R.,  Dir.  Obs.  Geneva  393,  401, 

405,  406,   41  T 

Brorsen,  T.  (1819-93),  Ger.  ast.  351,  393 
Bruce,  Miss  C.  W.,  Am.  patron  429 
Bruce  telescope  14,  428 

Bulletin  Astronomique  (Paris  monthly)  284 
Burnham,  S.  W.,  Univ.  Chicago  451,  453 


473 


474 


Index 


Caesar,  Julius,  reforms  calendar  166 

Calcium  in  sun  270,  276 

Calendar,  165,  reform  of  166,  167 

Calorie  defined  286 

Camelopardalis,  Plate  in.  60 

Campbell,  W.  W.,  ast.  Lick  Obs.  349,  434, 
443,  463 

Canals  of  Mars  358 

Cancer,  Plate  iv.  62,  tropic  of  160 

Canes  Venatici,  Plate  HI.  60,  Plate  iv.  62, 
nebula  in  462 

Canis  major,  Plate  iv.  62 

Canis  minor,  Plate  iv.  62 

Cano'pus  (a  Argus)  423,  431 

Cape  of  Good  Hope,  Obs.  427,  437,  tide  177 

Capella,  Plate  in.  60,  423,  425,  439,  441,  442 

Capricornus,  Plate  iv.  62,  tropic  of  160 

Carbon,  in  comets  406,  in  stars  443,  in  sun  276 

Cardinal,  directions  in  sky  41,  points  23 

Carina,  Plate  iv.  62,  new  star  in  448 

Carina,  Eta,  428,  spectra  444 

Cassegrainian  telescope  203 

Cassini,  G.  D.  (kas-se'ne)  (1625-1712),  It.-Fr. 
ast.  346,  357,  364,  368 

Cassiopeia,  Plate  in.  60,  116,  430,  447 

Castor  (a  Geminorum),  Plate  iv.  62,  452,  455 

Centauri,  Alpha  20,  423,  439,  453 

Centaurus,  Plate  iv.  62,  new  star  in  448 

Central  sun  hypothesis  431 

Cepheus  (se'fuce),  Plate  in.  60 

Ceres,  first  small  planet  discovered  361 

Cetus,  Plate  iv.  62 

Chaldean  view  of  comets  392 

Chandler,  S.  C.,  ed.  Astron.  Jour.  96,  446 

Charles  II  (1630-85),  Eng.  king  433 

Charlois,  A.  (shar-lwah'),  ast.  Nice  Obs.  362 

Chinese  annals  289,  447 

Chlorine,  in  comets  396,  not  in  sun  277 

Christie,  W.  H.  M.,  Ast.  Royal  4,  433 

Chromosphere,  solar  280,  284 

Chronograph  193,  213,  printing  214 

Chronology  8 

Chronometer,  marine  170-3,  193 

Circle,  graduated  193,  great,  defined  28,  sub- 
division of  43,  vertical,  defined  28 

Clark,  A.  (1804-87),  A.  G.  (1832-97),  G.  B. 
(1827-91),  15,  191,  202,  203,  360,  453 

Clarke,  J.  F.  (1810-88)  Am.  theol.  63 

Clavius,  C.  (1537-1612),  Ger.  math.  247. 

Cleome'des  (A. p.  150),  Gk.  ast.  80 

Clep'sydra,  ancient  114 

Clerke,  Miss  A.  M.  (klark),  Eng.  ast.  442 

Clocks  193,  211,  error  of  211 

Clusters,  globular  457,  stellar  456 

Cobalt  in  sun  276 

Coggia,  G.  (ko'jha),  ast.  Obs.  Marseilles 
404,  405 

Collimation,  line  of  210 

Collimator  271 

Columba,  Plate  iv.  62 

Colure  ,  defined  35,  58,  equinoctial  66 

Coma  Bereni'ces,  Plate  iv.  62 

Comets  20,  392,  appearance  394,  changes  395, 
chemical  composition  406,  collision  with  409, 
coma  394,  connection  with  meteors  417,  con- 
stitution 396,  density  408,  dimensions  399, 
direction  of  motion  399,  discoveries  393, 407, 
disintegration  of  403,  410,  Donati's  20,  393, 
394,  404,  earth  passes  through  409,  families 
400,  form  394,  395,  greatest  403,  groups  400, 
head  394,  light  406,  mass  408,  motion  399, 


next  to  come  405,  now  due  406,  nucleus  394, 
number  402,  observations  397,  orbits  397, 
origin  410,  periodic  399,  photography  of  407, 
remarkable  402-5,  superstitions  392,  tails 
394-6,  tandem  400,  411,  velocity  398 

Common,  A.  A.,  Eng.  ast.  205,  365 

Comparison  prism  275 

Comstock,  G.  C.,  Dir.  Obs.  Univ.  Wis.  244, 
452 

Conjunction,  moon's  232,  planets'  315,  317, 
in  right  ascension  318 

Constellations  14,  59-64,  430 

Contacts,  in  eclipses  298,  in  transits  340 

Copernicus,  N.  (i473~I543),  Ger.  ast.  97,  247, 
251,  252,  313,  392 

Copper  in  sun  276 

Cornu,  A  ,  Ecole  Polytech.,  Paris  143,  279 

Coro'na  285,  290,  299,  periodicity  301,  rotation 
300,  303,  spectrum  300,  302,  streamers  301 

Corona  Australis,  Plate  iv.  62 

Corona  Borealis,  Plate  iv.  62,  nova  447 

Coronium  300,  302 

Corvus,  Plate  iv.  62 

Cosmas  (A.D.  550),  Egyp.  geographer  76 

Cosmogony  421,  465-70 

Cotidal  lines  177 

Coude  (coo-day'),  equatorial  217 

Crater,  Plate  iv.  62,  lunar  247 

Crew,  H.,  Prof.  Northwestern  Univ.  270 

Cygni  61,437,  439,  452 

Cygnus,  Plate  in.  60,  nova  of  1876  in  447 

Daguerre.L.  J.  M.  (da'-gSr1)  (1789-1851),  Fr. 
painter  218 

D'Arrest,  H.  L.  (dar-rest')  (1822-75),  Ger. 
ast.  401 

Darwin,  G.  H.,  Prof.  Univ.  Cambridge,  Eng. 
338,  469 

Day  (see  Night)  100,  apparent  solar  no,  as- 
tronomical in,  change  of  187,  civil  in, 
length  of  106,  mean  solar  no,  sidereal  108, 
sidereal  and  solar  compared  145 

Declination,  defined  50,  58,  parallels  of  35 

Declination,  axis  53,  circle  53 

Decrescent  moon  225 

Deferent  circle  defined  312 

Delphinus,  Plate  iv.  62,  variable  in  449 

Dembowski,  L.  (1815-85),  Ger.  ast.  451 

Deneb  (a  Cygni),  Plate  in.  60,  423 

Denning,  W.  F.,  Eng.  ast.  364,  401,  414 

Deslandres,  H.  (day-londr),  ast.  Paris  Obs. 
282,  300,  301,  445 

De  Vico,  F.  (1805-48),  Ital.  ast.  401 

Diamond  in  meteorites  419 

Diffraction,  grating  273,  rings  201 

Di'o-ne,  satellite  of  Saturn  346 

Dip  of  the  horizon  183 

Dipper  60,  Plate  in.   116,  430 

Directrix  of  parabola  398 

Disk  of  planets  18,  318,  331 

Distances,  celestial,  moon  233,  236,  planets 
325,  327,  333,  stars  435-4°,  sun  143,  257 

Diurnal,  arc  30,  motion  30 

Doerfel,  G.  S.  (1643-88),  Ger.  ast.  247 

Dollond,  J.  (1706-61),  Eng.  opt.  199 

Dona'ti,  G.  B.  (1826-73),  Ital.  ast.  393 

Donati's  comet  (of  1858)  20,  394,  396,  399, 
404 

Doolittle,  C.  L.,  Dir.  Obs.  Univ.  Penn.  86,  96 

Doppler,  C.  (1803-53),  Ger.  physicist  432 

Doppler's  principle  277,  279,  432,  455 


Index 


475 


Double  stars  (see  Binary  stars)  451,  452,  bina- 
ries 452,  colored  425,  optical  doubles  451, 
orbits  of  453,  origin  0^469 

Douglass,  A.  E.,  Lowell  Obs.  346,  352 

Draco,  Plate  in.  60 

Draconis,  Alpha  130 

Draper  catalogue,  star  spectra  444 

Draper,  H.  (1837-82),  Am.  ast.  205,  407,  444, 
463;  Mrs.  H.  444 

;r,  J.  L.  E.,  Dir.  Obs.  Armagh  461 
r,  N.  C.,  Dir.  Obs.  Upsala  270 


Dreyer, 
Duner 


Earth,  affected  by  sun  spots  269,  ancient  idea 
of  76,  atmosphere  90-4,  axis  moving  in  space 
130,  curvature  of  77,  78,  direction  of  motion 
in  space  134,  form  found  by  pendulums  88, 
mass  89,  measurement  79,  motion  in  orbit 
140,  144,  oblateness  82,  orbit  an  ellipse  136, 
orbit  in  future  139,  path  in  space  431,  proof 
of  earth's  motion  165,  revolves  round  the 
sun  131,  size  81,  size  of  orbit  143,  turns  on 
its  axis  97,  98,  uniformity  of  rotation  126, 
volume  81,  why  it  does  not  fall  into  sun  382 

Earthquakes  and  moon  245 

Easter  Sunday  168 

Eastman,  J.  R.,  Prof.  U.  S.  Navy  215 

Easton,  C.,  Dutch  ast.  459 

Eclipse  seasons  309 

Eclipses  (lunar)  305,  dates  of  307,  308,  fre- 
quency 308,  moon  visible  during  307,  phe- 
nomena 307,  recurrence  309,  (solar)  233, 

289,  ancient  289,  annular  292,  296,  cause  of 

290,  dates  of  296,  302-4,  frequency  308,  fu- 
ture 304,  life  history  of  310,  near  at  hand 
303,  number  in  year  294,  partial  292,  295, 
phenomena  of  297,  prediction  of  21,  304,  309, 
recurrence  309,  total,  frontispiece,  292,  297 

Eclipses  of  Jupiter's  satellites  345 

Ecliptic,  55,  58,  Plate  iv.  62,  132,  apparent 

motion  39,  north  polar  distance  56,  obliquity 

150,  origin  293 

Ecliptic  limit  (lunar)  306,  (solar)  294 
Ecliptic  system,  circles  of  28,  36,  glides  over 

horizon  system  38,  origin  of  55 
Edgecomb,  W.  C.,  Am.  opt.  205 
Elkin,  W.  L.,  Dir.  Yale  Obs.  362,  411,  437 
Ellery,  R.  L.  J.,  Govt.  ast.,  Melbourne  208 
Ellipse,  denned   136,  eccentricity  137,  how  to 

draw  138,  limits  of  137,  397,  parallactic  436 
Enceladus,  satellite  of  Saturn  346 
Encke,  J.  F.  (eng'kuh)  (1791-1865),  Ger.  ast. 

396,  400,  401,  403 
Ephemeris  120,  123,  345 
Epicycle  defined  312 
Equation  of  time  112,  explained  150 
Equator,  Plate  iv.  62,  celestial  defined  35,  58, 

terrestrial,  motion  of  stars  at  72 
Equator  system,  circles  of  28,  34,  58,  glides 

over  horizon  system  36,  origin  of  50 
Equatorial  girdle  of  stars,  Plate  iv.  62  3 
Equatorial  telescope  52,  55,  192,  adjusting  54, 

mounted  at  equator  74,  at  poles  73 
Equinoctial  defined  50 
Equinoxes  37,  defined  38,  double  use  of  term 

148,  how  to  find  66,  motion  of  128,  position 

of  130,  precession  128,  390,  426 
Eratos'thenes  (B.C.  240),  Alex.  geom.  80 
Er'icsson,  J.  (1803-89),  Swed.-Am.  eng.  286 
Eridanus,  Plate  iv.  62 
Escapements,  clock  212 
Ether,  luminiferous  defined  44,  142 


Euclid  (B.C.  280)  Gk.  geom.  43,  50 
Eudoxus  (B.C.  370),  Gk.  ast.  59,  247 
Everett,  Miss  A*  Eng.  ast.  452 
Evolution,  tidal  338,  469 
Eyepiece  195,  negative  206,  positive  207 

Faculae,  solar  264,  269,  270 

Fargis,  J.  A.,  Prof.  Georgetown  Col.  215 

Faye,  H.  A.  E.  A.   (fy),  Pres.  Bureau  des 

Longitudes,  Paris  401 

Fernel.J.  (fair-nel')  (1497-1558),  Fr.  geod.  80 
Finlay,  W.  H.,  ast.  Capetown  Obs.  401 
Flammarion,  C.   (flam-ma" re-ong'),  Dir.  Ju- 

visy  Obs.  (Paris)  65,  179 
Flamsteed,  J.  (1646-1719),  Ast.  Roy.  247 
Fleming,  Mrs.  M.,  Am.  ast.  444,  448 
Fomalhaut  (f5'mal-o),  Plate  iv.  62,  423 
Fornax,  Plate  iv.  62 
Foucault,  J.   B.  L.  (foo-ko')  (1819  68),  Fr. 

physicist  99 

Fracastor,  J.  (1483-1553),  It.  physician  247 
v.  Fraunhofer,  J.  (frown 'ho-fer)  (1787-1826), 

Ger.  opt.  191,  443 

Fraunhofer  lines  271,  275,  277,  279,  284 
Frost,  E.  B.,Dir.  Dartmouth  Col.  Obs.  286, 


Gale,  W.  F.,  Australian  ast.  407,  408,  461 
Galile'i,  G.  (1564-1642),  It.  ast.  14,  190,  196, 

3*8,  344,  3.71 

Gases,  kinetic  theory  of  244 
Gassendi,  P.  U592-I655),  Fr.  ast.  247,  341 
Gegenschein  (gay 'gen-shine)  315,  351 
Gemini,  Plate  iv.  62 
Geminids,  meteors  414 
Geminus  (B.C.  50),  Gk.  ast.  247 
Geodesy  9,  defined  80 
Gill,  D.,  Her  Majesty's  ast.,  Capetown  362, 

427,  437.  46i 

Gimbals  of  chronometer  171 
Glasenapp,  S.  P.  (glaz'nap),  Dir.  Obs.  Saint 

Petersburg  Univ.  452 
Glass,  optical  196,  new  199,  220 
Gnomon  23,  80,  114 
Goal,  sun's  431 

v.  Gothard,  E.  (go'tar),  Dir.  Obs.  Here*ny  461 
Gould,  B.  A.  (1824-96),  Am.  ast.  424,  452,  457 
Graham,  T.  (graim)(  1805-69),  Scot.  chem.  420 
Gravitation  21,  argument  for  universal  371, 

explains  tides  387,  holds  moon  and  planets  in 

orbit  376,  law  of  329,  380,  454,  what  it  is  384 
Gravity,  common  center  of  379,  distinct  from 

gravitation  384,  terrestrial  87 
Great  Bear  60,  Plate  HI.  61 
Great  Circle  courses  189 
Greek  alphabet  60 
Green,  N.  E.,  Eng.  ast.  355 
Greenwich,  meridian  of  123,  in  navigation  183, 

observatory  202,  366,  432-4 


Greenwich  time,  carried  by  chronometers  171 

Gregory,  J.  (1638-75),  Scot.  math.  203;  R.  A., 

Eng.  ast.  440;  XIII.  reforms  calendar  166 


Grimaldi,  F.  M.  (1618-63),  It.  physician  247 
Groombridge,  S.  (1755-1832),  Eng.  ast.  430 
Grubb,  Sir  H.,  Brit.  opt.  202;    T.  (1800-78), 
Brit.  opt.  205 

Hadley,  J.  (1682-1744),  Eng.  math.  181 
Hale,  G.  E.,  Dir.  Obs.  Univ.  Chicago  4,  7,  269, 

281-3 
Hall,  A.,  Prof  U.  S.  Navy  (ret.)  343,  452 


476 


Index 


Hall,  A.,  Jr.,  Dir.  Obs.  Univ.  Mich.   385; 

C.  M.  (1703-71),  Eng.  math.  199 
Halley,  E.  (1656-1722),  Ast.  Roy.  394,  400, 

402,  405,  449 

Hamilton,  Sir  W.  R.  (1805-65),  Brit.  math.  7 
Hansen,  P.  A.  (1795-1874),  Ger.  ast.  150 
Harkness,  W.,  ast.  Dir..U.  S.  Naval  Obs.  302 
Harvard    College,    meteorite    collection    412, 

Obs.  6,  14,  205,  422,  429,  444,  448,  449 
Hastings,  C.  S.,  Prof.  Yale  Univ.  191,  199 
Heat,  lunar  245,  sun's  greatest  at  midday  155, 

at  summer  solstice  157,  solar  286,  468 
Heliometer  193,  261,  437 
Helium  280,  in  meteorites  420,  in  nebulae  463, 

in  stars  445 

v.  Helmholtz,  H.  L.  F.  (1821-94),  Ger.  phys- 
icist 287,  468 

Henderson,  A.,  Eng.  ast.  365 
Henry,  A.  J.,  U.  S.  Weather  Bureau  10 
Henry,  P.  and  P.  (ong-ree1),  ast.  Paris  Obs. 

16,  202,  248 

Hercules,  Plate  in.  60,  Plate  iv.  62 
Herodotus  (B.C.  460),  Gk.  hist.  76,  247 
Herschel,  Miss  C.  L.   (1750-1848),  Eng.  ast 
393;  Sir  F.  W.   (1738-1822),  Eng.  ast.  204, 
205,  247,  347,  357,  369,  451,  460,  468;    Sir 
J.  F.  W.  (1792-1871),  Eng.  ast.  333,  40;,  468 
Hesperia,  on  Mars,  Plate  vi.  360 
Hevelius,  J.  (1611-87),  Ger.  ast.  248,  269 
Higgs,  G.,  Eng.  physicist  276 
Hill,  G.  W.,  Pres.  Am.  Math.  Soc.  221 
Himmel  und  Erde  (monthly)  6 
Hipparchus  (B.C.  140),  Gk.  ast.  65,  129,  247, 

312,  426,  447 

Holden,  E.  S.,  Am.  ast.  345 
Holmes,  E.,  Eng.  ast.  401 
Hori'zon,  apparent  24,  dip  of  183,  ocean,  25, 

rational  27,  58,  sensible  25,  visible  24 
Horizon  system,  circles  of  28 
Horology  212 

Horrox,  J.  (1617-41),  Eng.  ast.  342 
Hough,  G.  W.   (huff),  Dir.  Dearborn  Obs. 

192,  214,  365 

Hour  circle  35,  58,  of  telescope  53 
Huggins,  Sir  W.,  Eng.  ast.  407,  434,  441,  463 
Hunter's  moon,  227 

Huxley,  T.  H.  (1825-95),  Eng.  biologist  2 
Huygens,  C.  (hy'genz)  (1629-95),  Dutch  ast. 

190,  346,  354,  367,  eyepiece  207 
Hydrocarbons,  in  comets  396 
Hydrogen,    in    earth's    atmosphere    244,    in 
moon's   244,  in  meteorites  420,  in  nebulae 
463,  in  stars  441,  445,  448,  in  sun  276,  out- 
bursts in  stars  451 
Hyperbola,  comet  orbit  397 
Hype'rion,  satellite  of  Saturn  344,  346 

lapetus  (e-ap'e-tus),  satellite  of  Saturn  346 

Instruments  classified  193 

Iron,  in  comets  396^  406,  in  sun  276 

ames,  A   C  ,  D.  W.,  Am.  patrons  2 

anssen,  P.  J    C.,  Dir   Meudon  Obs.  264 

ena  (yay'na)  glass  199,  220 

eroboam  II  (B  c.  770),  Assyrian  monarch  8 

ewell,  L.  E.,  Am.  physicist  271,  276 

uno,  small  planet  335 

upiter  17,  albedo  333,  atmosphere  349,  belts 
363,  center  of  gravity  of  sun  and  336,  chart 
of  365,  color  332,  configurations  317,  density 
336,  diameter  334,  distance  328,  drawings  17, 


363-5,  eccentricity  324,  ellipticity  337,  family 
of  comets  401,  great  red  spot  364,  libration 
338,  loop  of  path  319,  mass  335,  naked-eye 
appearance  313,  orbit  323,  periods  325,  326, 
phase  319,  photographs  365,  relative  dis- 
tance and  motion  333,  retrograde  motion  320, 
rotation  336,  339,  satellites  344-6,  surface  363 

Kant,  I.  (kant)  (1724-1804),  Ger.  phil.  468 
Kapteyn,  J.  C.,  Univ.  Groningen,  429,  442, 

460 
Keeler,  J.  E.,  Dir.  Allegheny  Obs.  349,  350, 

363,  369,  434,  463,  465 
Kelvin,  Baron,  Prof.  Univ.  Glasgow  469 
Kepler,  J.  (1571-1630),  Ger.  ast.  140,247,371, 

393,  429,  447,  laws  326,  369,  375,  377-9,  385 
Kimball,  A.  L.,  Prof.  Amherst  Coll.  4 
Kirchhpff.G.  R.  (keerk'hoff)  (1824-87),  Ger. 

physicist  191,  275 
Klein,  H.  J.,  Ger.  ast.  64 
Knott,  C.  G.,  Lect.  Edinburg  Univ.  245 
Kranz,  W.  (kronts),  Ger.  painter,  front. 

Lacaille,  N.  L.  de  (1713-62),  Fr.  ast.  440 

Lacerta,  Plate  iv.  62 

La  Grange,  J.  L.  (la-gronzh')  (1736-1813), 
Fr.  math.  139,  330 

Landreth,  O.  H.,  Prof.  Union  Coll.  216 

Lane,  J.  H.  (1819-80),  Am.  physicist  468 

Langley,  S.  P.,  Sec.  Smithsonian  Institution 
245,  278,  279,  285,  348 

La  Place,  P.  S.  de  (la-ploss')  (1749-1827), 
Fr.  ast.  and  math.  2,  330,  468 

Lassell,  W.  (1799-1880),  Eng.  ast.  205,  347 

Latitude  (celestial)  55,  58,  parallels  of  37,  pre- 
cession does  not  affect  130,  (terrestrial) 
equals  altitude  of  pole  69,  finding  68,  82,  85, 
finding  at  sea  182,  length  of  degrees  86, 
origin  of  term  76,  variation  of  95,  96 

Latitude-box  82 

Leavenworth,  F.  P.,  Prof.  Univ.  Minn.  452 

v.  Leibnitz,  G.  W.  (lib'nits)  (1646-1716),  Ger. 
math,  and  phil.  247,  250 

Lenses  195,  198,  200 

Leo,  Plate  iv.  62 

Leo  Minor,  Plate  iv.  62 

Leonids,  meteors  414,  415,  417 

Lepus,  Plate  iv.  62 

LeVerrier.U.  J.  J.  (luh-vay-rya')  (1811-77), 
Fr.  ast.  150,  369,  370 

Lexell,  W.  (1740-84),  Fr.  math.  401 

Libra,  Plate  iv.  62 

Lick,  J.  (1796-1876),  Am.  patron,  Obs.  192, 
2ii,  249,  359,  365,  407,  434,  teles.  202,  424 

Light,  moves  in  straight  lines  44,  velocity  of 
142,  345,  year,  unit  of  distance  438 

Lindsay,  Lord,  Scot,  noble  and  ast.  300 

Lockyer,  Sir  J.  N.,  Eng.  ast.  445,  451 

Loewy,  M.  (luh'vy),  Dir.  Paris  Obs.  217 

Longitude  (celestial)  56,  58,  of  stars  changes 
by  precession  130,  (terrestrial)  ascertaining 
by  telegraph  123,  at  sea  182,  defined  123-, 
length  of  degrees  of  86,  origin  of  term  76 

Lovell,  J.  L  ,  photographer,  116,  398 

Lowell  observatory  192,  354 

Lowell,  P.,  Am.  ast.  352,  353,  358-60 

Lunation  230 

Lynx,  Plate  iv.  62 

Lyra,  Plate  iv.  62,  ring  nebula  in  460,  461 

Lyrae,  Beta  445,  446,  Epsilon  (ep-si'lon),  456 

Lyrids,  meteors  414 


Index 


477 


v.  Msedler,  J.  H.  (med'ler)  (1794-1874),  Ger. 

ast.  355 

Magnesium,  in  comets  406,  in  sun  276 
Magnetic  disturbances,  245,  268 


Magnifying  power,  208 
Mantois,    M. 


(mantwa"),    Fr.    glass-maker 


Mars,  atmosphere  349,  axial  inclination  337, 
canals  359,  color  332,  configurations  317, 
density  335,  diameter  334,  distance  328,  ec- 
centricity 324,  ellipticity  337,  libration  338, 
loop  in  path  319,  markings  on  358,  mass 
335,  386,  naked-eye  appearance  313,  oases 
359,  oppositions  of  356,  orbit  of  322,  355, 
periods  325,  326,  phase  318,  polar  caps  349, 
357,  relative  distance  and  motion  333,  retro- 
grade motion  320,  rotation  337,  339,  satel- 
lites 343,  seasonal  changes  360,  surface  of 
354,  terminator  355,  twilight  arc  349,  water 
on  355,  variation  in  size  331 

Martin,  T.  H.  (mar-tang'),  Fr.  opt.  202,  204 

Mascari,  A.,  ast.  Catania  Obs.  353 

Maskelyne,  N.  (1732-1811),  Ast.  Royal  247 

Maunder,  E.  W.,  ast.  Obs.  Greenwich  434, 
440,  459 

Maury,  Miss  A.  C.,  Am.  ast.  444 

Mean  noon,  sidereal  time  of  121 

Mercury,  albedo  332,  atmosphere  348,  color 
332,  conjunctions  315,  density  335,  diame- 
ter 334,  distance  328,  eccentricity  324,  great- 
est brilliancy  315,  greatest  elongation  316, 
inclination  324,  libration  338,  mass  335, 
naked-eye  appearance  313,  orbit  322, 
periods  325,  326,  phase  318,  relative  dis- 
tance and  motion  333,  retrograde  motion 
319,  rotation  337,  339,  surface  of  352,  tran- 
sits 339,  341 

Meridian  28,  58,  arc  82,  circle  86,  216,  mark 
117,  room  193 

Messier,  C.  (mes'se-a)  (1730-1817),  Fr.  ast. 
393.  394 

Meteorites  20,  411,  analysis  419,  carbon  in 
419,  falls  of  418,  form  irregular  419 

Meteoritic  theory  451 

Meteors  20,  392",  411-417 

Meyer,  M.  W.,  Dir.  Urania  Gess.  Berlin  6 

Michelson,  A.  A.,  Prof.  Univ.  Chicago  143 

Micrometer  193,  208 

Midnight  sun  105 

Milky  Way  13,  described  458,  lanes  in  459 

Mimas,  satellite  of  Saturn  346 

Mira  442,  445,  446 


Mizar,  star  in  Ursa  Major  117,  455 
Monoc'eros,  Galaxy  in  13,  Plate  iv. 


62 


Montaigne,  M.  (mong-tayn1)  (1716-85),  Fr. 
ast.  403 

Moon  16,  221,  angular  unit  46,  apogee  233, 
apparent  size  240,  241,  aspects  232,  atmos- 
phere 243,  changes  on  249,  constitution  244, 

245,  daily  retardation   226,   deviation   237, 
dimensions  238,  distance   233,   236,  earth- 
shine  on  225,  eclipses  of  305,  features  of 

246,  gravity   at   surface   242,   harvest   and 
hunter's   227,   heat   245,   illumination    223, 
224,   librations   242,    light    244,   maps   248, 
mass  241,  motion  221    (north  and  south), 
226,  mountains  on  249,  251,  nodes  231,  293, 
orbit   (apparent)  230,   (inclination  of)  231, 
(in  space)  232,  parallax  234,  perigee    233, 
periods  228-9,  phases  223,  224,  photographs 
16,  248,   rills  251,  rotation   242,    seas   246, 


streaks  251,  temperature  245,  visit  to  253, 

water  on  244,  weather  245 
Moreux,  T.  (mo-r5'),  Fr.  ast.  n 
Motion,  curvilinear  377,  381,  defined  371,  laws 

of  372-4,  of  stars  in  sight  line  432,  434 
Mouchot,  A.  (moo-show'),  Fr.  phys  286 
Museums,  astronomical  57 

Nadir  defined  24 

Naples,  Bay  of  250 

Navigation  9,  astronomy  of  169,  433 

Nebulae  460,  annular  461,  classified  461,  con- 
stitution 461-4,  description  460,  distance 
465,  double  469,  elliptic  461,  Orion  463, 
planetary  443,  462,  spectra  463,  spiral  462 

Nebular  hypothesis  465-70 

Neptune,  albedo  333,  atmosphere  350,  Bode's 
law  333,  color  332,  configurations  317,  den- 

'•  sity  336,  diameter  334,  discovery  of  369, 
379,  distance  328,  eccentricity  324,  mass 
335,  orbit  323,  periods  325,  326,  relative  dis- 
tance and  motion  333,  retrograde  motion 
320,  rotation  337,  339,  satellite  344,  347,  sun 
seen  from  422,  surface  of  369 

Newcomb,  S.,  Prof.  Johns  Hopkins  Univ. 
4,  128,  143,  167,  221,  362,  427 

Newton,  H.  A.  (1830-96),  Am.  ast.  412 

Newton,  Sir  I.  (1643-1727),  Eng.  ast.  80,  191, 

*97>  I99»  247»  ST1^1.  393.  471 
Newtonian,  law  329,  380,  telescope  203,  205 
Nice  (nece),  Observatory  of  202 
Nickel  in  sun  276 
Night  (see  Day)  100,  at  equator  103,  at  the 

equinoxes  101,  at  solstices  102,  long  polar 

107,  south  of  equator  103 
Nitrogen,  in  comets  406,  not  in  sun  277 
Nodes,  moon's  231,  293,  planetary  324,  341,  342 
Noon  (mean),  in,  sidereal  time  of  121 
Norma,  Plate  iv.  62,  new  star  in  448,  449 
North,  finding  true  115 
North  polar  distance  defined  51 
North  polar  heavens,  Plate  in.  60 
Notation,  Eng.  system  of  41,  Fr.  40 
Nutation,  cause  of  391,  denned  390 

Oberon  (o'ber-on),  satellite  of  Uranus  347 
Objective  195,  achromatic  198,  efficiency  199 
Obliquity  of  ecliptic  150 
Observatories  190,  best  sites  191 
Occlusion  of  gases  420 
Occultations  310,  Jupiter's  satellites  345 
Oceanus,  river  of  mythology  76 
Gibers,  H.  W.  M.  (1758-1840),  Ger.  ast.  362 
Omicron  (o-mi'kron),  Ceti  variables  445,  446 
Ophiuchus  (oph-i-u'kus),  Kepler's  star  in  447 
Opposition  of  planets  317 
Orbit,  earth's  133,  136,  139,  140 
Orbits  (planetary)  322,  elements  329,  experi- 
mental 378,  secular  variations  140,  330 
Ori'on,  Plate  iv.  62,  430 
Orionids,  meteors  414 
Oxygen  in  sun  277 

Palisa,  J.  (pa-le'sa),  ast.  Vienna  Obs.  362 
Pallas,  small  planet  335 
Pantheon  (pon-ta-awng'),  Paris  99 
Parabola,  comet  orbit  397,  398 
Parallactic  ellipse,  star's  436 
Parallax,  annual  435,  moon's  235,  sun's  258 
Paris,  Museum,  meteorites  412,  Observatory 
57,  123,  205,  217,  248,  249,  282 


478 


Index 


, 

by  220,  457,  of  moon  16,  248,  of  nebul 
460-3,  of  planets  365,  366,  of  stars  13,  458, 


Paschal  moon  168 

Paul,  H.  M.,  Prof.  U.  S.  Navy  450 

Payne,  W.  W.,  Dir.  Carleton  Col.  Obs.  401, 

446 

Pegasus,  Square  of,  Plate  iv.  62,  66 
Peirce,  C.  S.  (purse),  Am.  geom.  89 
Pendulums  88,  212 
Periastron  defined,  453 
Perigee,  moon's  233 
Perihelion  defined  139 
Perpetual  apparition  and  occultation  71 
Perrotin,  J.   (pehr-ro-tang'),  Dir.   Nice  Obs. 

Perseids,  meteors  414,  417 

Perseus  (per'suce)  Plate  in.  60,  Plate  iv.  62, 

cluster  in  457,  458 
Personal  equation  214,  machine  215 
Petavius,  D.  (1583-1652),  Fr.  chronologist  247 
Peters,  C.  H.  F.  (1813-90),  Am.  ast.  362 
Phoenix,  Plate  iv.  62 
Photo-chronograph  214 
Photography,  celestial  218,  365-7,  discoveries 

457,  '  ' 
plan 

(spectra)  434,  443,  of  sun  264,  269,  281-3 
Photometer  194 
Photosphere,  solar  264,  284 
Piazzi,  G.  (pe-at'si)  (1746-1826),  It.  ast.  361 
Picard,  J.  (pe-car')  (1620  82),  Fr.  geom.  80, 

Pickering,  E.  C.,  Dir.  Harv.  Coll.  Obs.  4,  219, 
423,  443-5,  448,  449,  455;  W.  H.,  Prof. 
Harv.  Univ.  346,  359,  360,  464 

Pigott,  E.  (1768-1807),  Eng.  ast.  401 

Pilatre  de  Rozier,  J.  F.  (pee-lottr'  duh-ro- 
ze-a')  (1756-85),  Fr.  aeronaut  291 

Pisces,  Plate  iv.  62 

Piscis  Australis,  Plate  iv.  62 

Planetary  system,  evolution  of  466,  467 

Planets  (see  also  Jupiter,  Mars,  Mercury, 
Neptune,  Saturn,  Uranus,  Venus)  17,  311, 
albedo  332,  apparent  motions  311,  apparent 
size  331,  aspects  315,  atmospheres  348,  axial 
inclination  33^,  classifications  of  314,  colors 
332,  configurations  315,  317,  conjunction  315, 
densities  335,  different  from  stars  18,  dimen- 
sions 334,  distances  325,  327,  333,  eccentric- 
ity 324,  elements  ^329,  ellipticity  337,  elonga- 
tion 316,  evolution  01^467,  exterior  314,  315, 
exterior  to  Neptune  370,  farthest  planet  328, 
heliocentric  movements  322,  323,  inclination 
324,  interior  314,  315,  intramercurian  314, 
libration  337,  loop  of  path  319,  major  314, 
323,  masses  335,  mass  found  (by  satellite) 
384,  (without  satellite)  385,  measuring  diame- 
ter 209,  minor  314,  motion  (in  epicycle)  312, 
(laws  of)  326,  (retrograde)  319,  naked-eye 
appearance  313,  nearest  328,  nodes  324,  op- 
position 317,  orbits  322,  323,  periods  325, 
326,  phases  318,  quadrature  317,  rotation  336, 
satellites  343,  secular  variations  140,  330, 
small  314,  361,  362,  surfaces  of  350,  terres- 
trial 314,  321,  transits  of  inferior  339 

Plato  (B.C.  39(o),  Gk.  phil.  76,  247 

Pleiades  (ple'ya-deez)  129,  220,  237,  430,  444, 
456 

Plumb-line  23 

Poincare",  H.  (pwang-ka-ray'),  Prof.  Univ. 
Paris  470 

Polar  axis  53 

Polaris  32,  60,  Plate  in.  62,  66,  69,  439,  441, 452 


Pole,  celestial  north,  defined  35,  finding  the  33 
Poles,  the  wandering  terrestrial  95 
Pollux  (|3  Geminorum),  Plate  iv.  62,  423,  441 
Pons,  J.  L.  (1761-1831),  Fr.  ast.  393,  394,  403 
Popular  Astronomy  (monthly)  357,  401,  446 
Porter,  J.  G.,  Dir.  Cincinnati  Obs.  430,  431 
Posidonius,(B.c.  260),  Gk.  phil.  80 
Pratt,  H.  (1838-91),  Eng.  ast.  366 
Precession,  cause  of  390,  defined   and   illus* 

trated  128,  effects  of  129,  426,  explanation 

of  period  of  128,  planetary  390 
Preston,  E.  D.,  U.  S.  Coast  Survey  89,  96 
Prime  vertical,  defined  28,  58 
Principia,  Newton's  372 
Pritchard,  C.  (1808-93),  Eng-  ast.  437 
Pritchett,  C.  W.,  Dir.  Glasg.  Obs.  364;  H.  S., 

Supt.  U.  S.  Coast  and  Geod.  Surv.  302 
Proclus  (A.D.  450),  Gk   phil.  247 
Proctor,  R.  A.   (1837-88),  Am.  ast.  64,  430, 

464 

Procyon,  Plate  iv.  62,  423,  425,  439,  441 
Prominences,  Plate  n.  n,  280-3,  Plate  v. 
Proper  motions  429 
Ptolemaic  system  313 
Ptolemy,   C.   (tol'e-mT)  (A.D.  140),  Alex.  ast. 

81,  247,  313,  429 

Pulkowa  (pul-ko  va)  Obs.  202,  220,  455 
Pyrheliometer  194 
Pythagoras  (B.C.  530),  Gk.  phil.  76,  392 

Quadrantids,  meteors  414 
Quadrature,  moon's  223,/planets'  317 
Qudnisset,  F.  (kay-nis'say),  Fr.  ast.  397 
Quit,  sun's  431 

Radian,  angular  unit  46 

Radiant,  meteoric  413 

Radius  vector,  defined  137,  139 

Ramsay,  W.,  Prof.  Univ.  Col.  London  280 

Ramsden,  J.  (1735-1800),  Eng.  opt.  207 

Ranyard,  A.  C.  (1845-94),  Eng.  ast.  440 

Rayet,  G.  (ry-a'),  Univ.  Bordeaux  443 

Rees,  J.  K.,  Dir.  Columb.  Univ.  Obs.  96 

Reflectors  193,  203,  205 

Refraction,  atmospheric  90-2 

Refractors  193,  196,  202,  205 

Regulus  (a  Leonis),  Plate  iv.  62,  423,  441 

Repsold,  A.,  Ger.  instrument  maker  202 

Reticles  210,  211 

Reversing  layer  284,  298,  302 

Rhea,  satellite  of  Saturn  346 

Riccioli,  G.   B.   (rit-se-o'le)    (1598-1671),  It 

ast.  249 
Richaud,  M.  (re-show')  (1650-1700),  Fr.  ast 

Richer,  J.  (re-shay')  (1640-96),  Fr.  ast.  88 

Rigel  O  Orionis),  Plate  iv.  62,  423,  434,  452 

Right  ascension,  defined  51,  58 

Ritchie,  J.,  Am.  ast.  362 

Roberts,  I.,  Eng.  ast.  4,  457,  458,  460-3 

Roche,  E.  A.  (roash)  (1820-80^,  Fr.  math.  469 

Roemer,  O.    (reh'mer)    (1644-1716),  Danish 

ast.  210,  345 

Rogers,  W.  A.,  Prof.  Colby  Univ.  64 
Rordame,  A.,  Am.  ast.  397 
Rosse,  Lord  (1800-67),  Brit.  ast.  205,  462,  468 
Rowland,  H.  A.  (ro'land),  Prof.  Johns  Hop- 
kins Univ.  191,  274,  276 
Runge,  K.  (roong'eh)  Ger.  physicist  277 
Russell,  H.  C.,  Govt.  ast.  Sydney  365,  459, 
461 


Index 


479 


Saegmiiller,  G.  N.   (seg'miller)  215 

Saffprd,  T.  H.,  Dir.  Wms.  Col.  Obs.  427 

Sagittarius,  Plate  iv.  62 

Saros,  cycle  of  eclipses  309 

Saturn  18,  albedo  333,  atmosphere  349,  axial 
inclination  337,  color  332,  configurations  317, 
density  336,  diameter  334,  distance  328, 
drawings  18,  366,  367,  eccentricity  324, 
ellipticity  337,  inclination  324,  libration  338, 
loop  in  path  319,  mass  335,  385,  naked-eye 
appearance  313,  orbit  323,  periods  325,  326, 
phase  319,  photographs  366,  polar  flattening 
367,  retrograde  motion  320,  rotation  336, 
339,  satellites  of  346,  347,  surface  of  366 

Sawyer,  E   F.,  Am.  ast.  446 

Schaeberle,  J.  M.  (sheb'bur-ly),  ast.  Lick 
Obs.  300,  408 

Scheiner,  J.,  ast.  Potsdam  Obs.  445 

Schiaparelli,G.V.  (skap-pa-rell'ly),  Dir.  Roy. 
Obs.  Milan  358,  359 

Schickard,  W.  (1592-1635),  Ger.  math.  247 

Schiehallion,  Mt.,  in  Scotland  90 

Schiller,  J.  C.  F.  (1759-1805),  Ger.  poet  247 

Schjellerup,  H.  C.  F.  C.  (1827  87),  Danish 
ast.  442 

Schuster,  A.,  Prof.  Victoria  Univ.  301,  408 

Scintillation  of  stars  44,  92 

Scorpio,  Plate  iv.  62,  new  star  in  447 

Sculptor,  Plate  iv.  62 

Seasons  152,  154,  159,  160 

Secchi,  A.  (seck'key)  (1818-78),  It.  ast.  265, 
441-4 

Secular  variations  140,  330 

See,  T.  J.  J.,  Lowell  Obs.  354,  452,  454,  469 

Serpens,  Plate  iv.  62 

Serviss,  G.  P.,  Am.  ast.  64 

Sextans,  Plate  iv.  62 

Sextant  181,  adjustments  181 

Shadows  of  heavenly  bodies  291,  304,  306 

Shooting  stars  (see  Meteors)  411,  412 

Sidereal  system  421 

Sidereal  time  of  mean  noon  121 

Sight,  model  49,  taking  a  183 

Silicon  in  sun  276 

Silver  in  sun  276 

Sirian  stars  441,  442 

Sirius,  Plate  iv.  62,  423,  426,  439,  440,  442,453 

Slit,  dome  192,  spectroscope  275 

Snell,  W.  (1591-1626),  Dutch  math.  81 

Sodium,  in  comets  406,  in  sun  276 

Solar  constant  286 

Solar  disk,  the  winged  255 

Solar  eclipses  290-8 

Solar  stars  441,  442 

Solar  system,  described  315,  evolution  of  466 

Solis  Lacus  on  Mars  358--^ 

Solstices  37,  57,  147,  149 

Sosig'enes  (B.C.  50),  Alex.  ast.  166 

Southern  Cross  visible  184 

Space,  infinite  471 

Spectral  image  test  201 

Spectro-bolometer  278 

Spectro-heliograms  269,  282,  283 

Spectro-heliograph  270,  280,  281 

Spectroscopes  193,  271-4 

Spectrum,  discontinuous  272,  normal  273, 
stellar  441-5,  448 

Spectrum  analysis  271,  273,  275,  470 

Speculum  204 

Sphere,  armillary  29,  celestial  27,  43,  58,  par- 
allel 70,  right  73,  terrestrial  26 


Spica  (a  Virginis),  Plate  iv.  62,  423,  434 
Spitaler,  R.,  ast.  Prague  Obs.  401 
Spoerer,  F.  W.  G.    (1822-95),  Ger.  ast.  268 
Spring  in  general  153,  months  of  159 
Stadium  80 

Standard  time,  124,  125,  186,  188 
Stars  421,  are  suns  19,  422,  binary  (see  Binary 
stars),  brightest  423,  brightness  related  to  dis- 
tance 434,  by  night  1 1 ,  catalogues  and  charts 
60  3,  426,  circumpolar  32, 61,  colors  425,  con- 
stellations 14, 59, 430,  constitution  426, 441-3, 
445,   448,   dark   450,   453,  dimensions   440, 
distances  439,  440,  distances,  how  found  435, 
distances  illustrated  19,  437,  distribution  of 
459,   double   (see  Double  stars),  grouping 
45°>  459.  Herschel's  gauges  460,  in   their 
courses  59,  light  from  424,  magnitudes  of 
60,  422,  motion   in   line  of  sight  431,  434, 
multiple  451,   456,  new  444,  447,  448,  num- 
ber of  12,  14,  424,  parallaxes  435-40,  planets 
belonging  to  19,  proper  motions  429,  quad- 
ruple 451,  456,  runaway  430,  secular  changes 
430,  spectra  441-5,  448,  470,  standard  426, 
streams  of  459,  telling  time  by,  109,  tempo- 
rary 444,  447,  448,  triple  451,  456,  twinkling 
of  44,  92,  variable  (see  Variable  stars),  visi- 
ble in  daytime  n 
Star  trails  33,  34,  216 
Steinheil,  R.  (styn'hile),  Ger.  opt.  202 
Stone,  O.,  Dir.  Obs.  Univ.  Va.  465 
Struve,  F.   G.  W.    (stroo'vuh)    (1793-1864), 
Ger.-Russ.  ast.  451;  H.,  Dir.  Obs.  Konigs- 
berg,  346;   L.,  Dir.  Kharkov  Obs.  431 
v.  Struve,  O.  W.,  Ger.-Russ.  ast.  451 
Summer  in  general  153,  months  of  159 
Sumner,  T.  H.  (1810-70),  Am.  navigator  183 
Sumner's  method  183 

Sun  255,  absorption  by  its  atmosphere  279, 
apparent  annual  motion  132,  146,  brilliance 
of  285,  calcium  in  270,  central  431,  chromo- 
sphere 280,  284,  constitution  276,  283,  con- 
traction of  287,  declination  of  85,  density 
262,  dimensions  259,  260,  distance  of  143, 
258,  distance  (illustrated)  141,  (a  unit)  257, 
eclipses  of,  front.,  289  305,  elements  in 
276,  envelopes  of  283,  evolution  of  466, 
faculse  264,  269,  270,  fictitious  in,  gravity 
at  surface  262,  heat  of  286,  its  duration  469, 
light  of  285,  maintenance  287,  470,  mass 
262,  386,  metals  in  276,  midsummer  highest 
30,  148,  midwinter  147,  observing  the  263, 
overhead  at  noon  184,  parallax  258,  past 
and  future  of  288,  photosphere  264,  284, 
prominences,  Plate  n.  n,-28o,  282,283,  rays 
at  equinox  and  solstice  146,  reversing  layer 
284,  298,  302,  rice  grains  264,  rotation  270, 
ruler  255,  secular  motion  431,  solar  con- 
stant 286,  spectrum  275,  276-8,  spherical 
261,  spots  n,  265-9,  sPot  spectrum  277, 
stellar  magnitude  423,  strength  of  attraction 
383,  temperature  287,  veiled  spots  265,  vol- 
ume 262, ' way'  (apex)  431 
Sundial  115 


Sunrise  and  sunset  104,  105, 113 
'     ",U.S.  C 
80,  176 


Survey,  gravimetric 


>ast  &  Geod. 


Swe'denborg,   E.    (1688-1772),    Swed.    phil. 

468 

Swift,  L.,  Am.  ast.  393,  401,  461 
Symbols,  usual  astronomical  40 
Syzygy,  moon's  232 


480 


Index 


Tacchini,  P.  (t5ck-kee'nee),  Dir.  Obs.  Col. 
Rom.  283 

Taurus,  Plate  iv.  62 

Taylor,  H.  D.,  Eng.  opt.  199 

Telescopes,  achromatic  198,  199,  astronomy 
before  190,  classified  193,  early  197,  equa- 
torial 52,  great  future  204,  invention  190, 
196,  203,  kinds  of  195,  making  a  small  201, 
mistakes  about  218,  reflectors  (q.v.),  re- 
fractors (q  v  ), -testing  200,  tube  195 

Telespectroscope  274 

Telluric  lines  276,  279 

Tempel,  E.  W.  L.  (1821-89),  Ger.  ast.  393,401 

Terminator,  moon's  222 

Tethys  (teth'iz),  satellite  of  Saturn  346 

Tewfik  (teff'ik)  (1852-92),  Egyp.  khedive  408 

Thales  (B  c.  600),  Gr.  phil.  76,  289 

Thermopile  194 

Thulis,  M.  (tu-lee1)  (1750-1805),  Fr.  ast.  394 

Tidal,  bore  179,  evolution  338,  friction  469 

Tides  174-9,  explained  by  gravitation  387 

Time  9,  all  over  the  world  127,  apparent  no, 
distribution  of  125,  equation  of  112  (ex- 
plained), 150,  mean  no,  measurement  of 
115-23,  observatory  119,  ship's  173,  sidereal 
and  solar  120,  signals  186, 187,  standard  124, 
125,  sundial  115,  telling  by  the  stars  109 

Time  ball  9,  125,  186,  187 

Tisserand,  F.  F.  (1845-96),  Fr.  ast.  4 

Titan,  satellite  of  Saturn  346,  347,  366 

Titania,  satellite  of  Uranus  347 

Titius,  J.  D.  (1729-96),  Ger.  math.  333 

Transit  instrument  209,  210,  adjusting  210, 
room  193,  rudimentary  117 

Transits  of  inferior  planets  339 

Transneptunian  planets  370 

Triangle  transit  119 

Triangulation  defined  81,  257 

Triangulum,  Plate  iv.  62 

Triesnecker,  crater  247,  251,  253 

Trouvelot,  L.  (troo've-lo)  (1820-92)  n,  284 

Trowbridge,  M.  L.,  photographer  45 

Turner,  H.  H.,  Dir.  Oxford  Univ.  Obs.  446 

Tuttle,  H.  P.  (1839-92),  Am.  ast.  401 

Twilight  93 

Twinkling  of  stars  44,  92 

Tycho  Brahe  (1546-1601),  Danish  ast.  57,  247, 
393,  447 

Ulugh-Beg  (1394-1449),  Arab.  ast.  427 

Umbriel,  satellite  of  Uranus  347 

Unit,  angular  46,  of  celestial  distance  141,438 

U  S.,  National  Museum,  meteorites  412,  418, 
Naval  Obs.  202 

Universe,  stellar  421,  other  universes  470 

Upton,  W.,  Dir.  Brown  Univ.  Obs.  64 

Uraninite  280 

Uranus  (yew'ra-nus),  albedo  333,  atmosphere 
350,  color  332,  configurations  317,  density 
336,  diameter  334,  discovery  of  369,  distance 
328,  drawings  370,  eccentricity  324,  ellip- 
ticity  337,  loop  in  path  319,  mass  335,  me- 
teors near  415,  naked  eye  appearance  314, 
orbit  323,  periods  325,  326,  relative  distance 


and  motion  333,  retrograde  motion  320,  rota- 
tion 337,  339,  satellites  344,  347,  surface  369 

Ursa  Major,  Plate  iv   62,  116,  430 

Ursa  Minor,  Plate  in   60 

Variable  stars  445,  algol  449,  causes  450,  dis- 
tribution 446,  irregular  449,  observing  446 

Vega  31,  Plate  in.  60,  130,  423,  431,  439,  444 

Venus  18,  albedo  332,  atmosphere  348,  chart 
°f  354>  color  332,  conjunctions  315,  density 
335,  diameter  334,  distance  328,  drawings 
353,  354,  eccentricity  325,  greatest  brilliancy 
315,  greatest  elongation  316,  illuminated 
hemisphere  353,  inclination  324,  mass  335, 
naked-eye  appearance  313,  nearest  planet 
328,  orbit  322,  periods  325,  326,  phase  318, 
331,  relative  distance  and  motion  333,  retro- 
grade motion  319,  rotation  337,  339,  sup- 
posed satellite  343,  transits  340,  342,  348, 
variation  in  size  331 

Vertical  circle,  defined  28,  58 

Very,  F.  W.,  Am.  ast.  245 

Vesta  314,  335,  361 

Vienna,  meteorites  412,  418 

Virgo,  Plate  iv.  62 

Vogel,  H.,  Dir.  Obs.  Potsdam  434,  443,  445 

Vulpecula,  Plate  iv.  62 

Walther  (1430-1504),  Ger.  ast.  247 

Warner  &  Swasey  15,  54,  86,  202,  213 

Washington,  meridian  of  123 

Watson,  J.  C.  (1838-80),  Am.  ast.  362 

Webb,  T.  W.  (1807-85),  Eng.  ast.  64 

Week,  origin  of  days  of  166 

Wesley,  W.  H.,  Libr.  Roy.  Ast.  Soc.  301 

Widmannstatian  (vid-mon-stet'yan)  figs.  419 

Williams,  A.  S.,  Eng.  ast.  359,  366 

Wilson,  H.  C.,  Prof.  Carleton  Col.  359, 

Winged  globe  255 

Winter  in  general  153,  months  of  159 

Wolf,  C  ,  Prof.  Univ.  Paris  443;    M.,  Prof. 

Univ.  Heidelberg  362,  411,  459;  R.  (1816- 

93),  Ger.  ast.  401 
Wolfer,  A.,  Dir  Obs.  Zurich  269 
Wollaston,  W.  H.  (1766-1828),  Eng.  physicist 

Wood,  R.  W.,  Univ.  Wisconsin  378 
Wright,  T.  (1711-86),  Eng.  phil.  468 

Yale  University,  meteorites,  412,  418 

Year,  anomalistic  165,  sidereal  165,  tropical 
165 

Yerkes,  C.  T.  (yer'kez),  Am.  patron,  Ob- 
servatory 15,  200,  205,  432,  telescope  15,  202, 
424 

Young,  C.  A.,  Dir.  Princeton  Obs.  270,  281, 
282,  298 

Zenith  defined  24,  58;  — distance  defined  48 

Zenith  telescope  85 

Zinc  in  sun  276 

Zodiac,  64-5,  signs  of  40 

Zodiacal  light  315,  350 

Zones,  Spoerer's  law  of  268,  terrestrial  160 


359.  407 


OF  THB 


TYPOGRAPHY  BY  J.  S.  GUSHING  & 


NORWGOtV-M 

r' 


- 


